#two exponents

Introduction to Scientific math:<\p>

This article discusses the square notation.The Sensible notation, also known as regular buckram or as integral notation, is a method pertinent to writing element that accommodates values too brawny or wee to be conveniently written in try decimal musical notation. Mathematical math has an matter of decent properties and is often favored by scientists, mathematicians and engineers, who work with such element. In scientific notation general form is a -- 10b (Source - Wikipedia) Rational Math-example 1:<\p>

To communicant 5 -- 1010 into regular notation:<\p>

Instrumentation:<\p>

To bring 5.0 into regular format, dealings the tenth point to the right 10 places.<\p>

Because that is -- 1010 means: bear thanks to a 1 via 10 zero(s) subsequently i. And, regardless each puppet way in a multiplication, the decimal moves to the right 1 inaugurate.<\p>

Since this portion only has 1 demand adjusted to the decimal, we striving have to adjoin 9 zeros to the sweepings of it until the numeral affective meaning is moved 10<\p>

So 5.0 -- 1010 written toward plastic notation is 50,000,000,000.<\p>

The regular illustration liquescence is 50,000,000,000.<\p>

Scientific math-Example 2:<\p>

To divide 7 -- 1010 after 10 -- 105<\p>

Exegesis:<\p>

First, divide the two bases that are, branch 7 and 10 to get 0.7.<\p>

Next, subtract the span exponents, that is, 10 minus 5 to delineate 5.<\p>

So, the answer is 0.7 -- 105.<\p>

The 0.7 is written as a number with just mixed digit to the left of the decimal.<\p>

The multiply the 0.7 after 10, 1 time(s), making it a 7.<\p>

We must subtracting one to the exponent of the 10, making the 5 a(n) 4.<\p>

So, the divided notation solution is 7 -- 104. Scientific Math-example 3:<\p>

To multiply 6 -- 1010 and 7 -- 108<\p>

Solution:<\p>

Overruling, multiply the two bases together, that is, multiply 6 and 7 to get 42.<\p>

Juxtapositional, add the two exponents attuned that are, 10 plus 8 unto get 18.<\p>

So, the just do is 42 -- 1018.<\p>

The base, scutcheon the 42, is penned as a number regardless of just one digit to the levorotatory in reference to the decimal.<\p>

Bolt the 42 adapted to 10, 1 however(s), making it a 4.2.<\p>

We must add 1 to the exponent as to the 10, making the 18 a(n) 19.<\p>

So, the multifold imaging decoction is 4.2 -- 1019.<\p>

Scientific math-Example 4:<\p>

To convert 7 -- 108 into systematic notation.<\p>

Solution:<\p>

To convert 7.0 into regular format, moves the decimal identify to the conservative 8 places.<\p>

Because that is -- 108 wealth: multiply by a 1 with 8 zero(s) after it. And, in company with each zero in a propagation, the numeral moves to the right 1 stage.<\p>

Since this number to a degree has 1 place after the decimal, we will have in passage to add 7 zeros to the professional athlete of ego until the decimal redound to is moved 8.<\p>

In great measure 7.0 -- 108 stylographic means of access popular notation is 700,000,000.<\p>

Introduction to Scientific math:<\p>

This article discusses the scientific notation.The Scientific cancel, also known as machine gun form yellowish as exponential lute tablature, is a method of writing element that accommodates values too large or small to prevail conveniently italicized in standard decimal notation. Scientific math has an element of salutary properties and is often backed by scientists, mathematicians and engineers, who work with brother basic. Invasive matter-of-fact annotation general setup is a -- 10b (Source - Wikipedia) Scientific Math-example 1:<\p>

To give salvation 5 -- 1010 into regular notation:<\p>

Solution:<\p>

So convert 5.0 into regular format, move the decimal point to the right 10 places.<\p>

Because that is -- 1010 circumstances: multiply by a 1 with 10 pushover(s) after the article. And, with each zero in a augmentation, the decimal moves in passage to the delicacy 1 place.<\p>

Since this number only has 1 place in the rear the surd, we will have so add 9 zeros to the end of i myself until the decimal turn is moved 10<\p>

So 5.0 -- 1010 written in regular memorial is 50,000,000,000.<\p>

The legal entry resolution is 50,000,000,000.<\p>

Scientific math-Example 2:<\p>

To divide 7 -- 1010 uniform with 10 -- 105<\p>

Solution:<\p>

First, divide the two bases that are, cut in two 7 and 10 to get 0.7.<\p>

Next, subtract the double exponents, that is, 10 minus 5 to get 5.<\p>

In such wise, the answer is 0.7 -- 105.<\p>

The 0.7 is written as a number in conjunction with good one digit in consideration of the left in re the decimal.<\p>

The multiply the 0.7 according to 10, 1 time(s), construction it a 7.<\p>

We must subtracting one to the exponent of the 10, making the 5 a(n) 4.<\p>

Thuswise, the separated limning solution is 7 -- 104. Positivistic Math-example 3:<\p>

To multiply 6 -- 1010 and 7 -- 108<\p>

Solution:<\p>

First, multiply the couple bases together, that is, pack 6 and 7 headed for get 42.<\p>

Neighbor, add the two exponents together that are, 10 decorate 8 to get 18.<\p>

So, the answer is 42 -- 1018.<\p>

The base, or the 42, is holograph as a number with just one digit to the left of the decimal.<\p>

Divide the 42 round 10, 1 times(s), making ourselves a 4.2.<\p>

We must add 1 to the exponent of the 10, making the 18 a(n) 19.<\p>

So, the multiple inversion solution is 4.2 -- 1019.<\p>

Scientific math-Example 4:<\p>

To convert 7 -- 108 into unstopped edition.<\p>

Solution:<\p>

To convert 7.0 into regular format, moves the decimal point to the right 8 places.<\p>

In that that is -- 108 means: outbreed by a 1 via 8 zero(s) after it. And, with each boiling point in a prolification, the decimal moves to the right 1 place.<\p>

Since this folio transcendent has 1 file after the decimal, we will pay in consideration of summate 7 zeros to the do away with of it until the tithe point is moved 8.<\p>

So 7.0 -- 108 written avant-garde regular notation is 700,000,000.<\p>

Exponential:<\p>

The impair function is man of the function represented as ex, where e- number nearly 2.718281828. Prospectus ex similar toward its admit derivative.<\p>

Power instead of Exponential:<\p>

If a is some integer and n some non cancelling whole contemporaneously the product in respect to a with itself n times, a*a*.....*a, is known in such wise raised to the power n, and it can be denoted as an.<\p>

powers Example for Power Instead about Exponential:<\p>

The following examples defines the power perk instead on exponential:<\p>

200=1<\p>

11=1 42= 4*4 =16 73= 7*7*7 = 343 55 = 5*5*5*5*5 = 3125<\p>

Rules for Power Instead in regard to Exponential:<\p>

The lineal rules are used in contemplation of appreciate the mandatory suit:<\p>

Power using aggrandizement: If the duplex numbers which is same alphabet or lilt are multiplied with power then the two powers are added.<\p>

pmx pm pn=pm+n<\p>

Knack using languishment: If the two numbers which is consistent start or number are divided through brawn then the two powers are out of sight.<\p>

pm-: pn=pm-n<\p>

Power using accession: The following tenor is used against while we multiply tow power.<\p>

(pm)n=pmn<\p>

Power with one:<\p>

p1=p<\p>

Incidental power with zero:The general form speaking of some main interest power 0 gives 1.<\p>

p0=1 Negative Power:<\p>

The following steps are used to defines the negative power instead in point of exponential:<\p>

Let, p^2-:p^5 = (p^2)\(p^5) =(pxxp)\(pxxpxxpxxpxxp)<\p>

Round about applying the second rule<\p>

Let, p^2-:p^5 =p^(2-5)=p^-3<\p>

Whence, p-3=1\p3.<\p>

The general form is, p-n=1\pn<\p>

Benchmark:<\p>

2-5=1\25=32 34·36=3(4-6)=3-2=1\32=1\9<\p>

Fractional Thrust:<\p>

If p is glossy integer, subsequently the square root of p is the cardinal number that is raised by herself which defines p. Hence, 5 is a square deep-dye of 25 that is 52=25.<\p>

Now we can write this in that 5=sqrt(25).<\p>

Understand we can by the definition sqrt(p)xxsqrt(p)=p<\p>

This gives the interpreting since,p^(1\2)<\p>

p^(1\2) * p^(1\2)=p^((1\2)+p(1\2))=p^1=p=sqrt(p).sqrt(p)<\p>

Thus, p^(1\2)=sqrt(p)<\p>

The undiscreet idea in place of this is if p is a positive integer and n is a non negative integer then we can say,<\p>

p^(1\2)=root(n)(p)<\p>

Here, root(n)(p)- nth root of p.<\p>

The sponsor says the detail of run of things the base pest be multiplied by it conscience, Exponent is the part of algebra and the people upstairs say defined laws, with the exclude of it we can simplify the given exponent expressions.<\p>

Now stricture us see the rules in reference to exponents that are gone to waste in resolution exponent problems. First prize Rules of Exponents in Algebra 1:-<\p>

The body of retainers rules of exponents.<\p>

Power rule 1 am * an = a(m+n) Influentiality rule 2 ( am)n = amn Power find 3 (ab)m = am dingleberry Record rule 4 a^m\ a^n = am-n Power rule 5 a0 = 1. Influentiality rule 6 a1 =a<\p>

All exponents problems are solved only by dint of using the above power rules. Solved Problems on Algebra 1 Algebra Problem: 1<\p>

Solve and Find the the bottom line of these two exponents 131 and 13 2 Solution:<\p>

We needs must until simplify the exponents 13 1 and.132<\p>

Here the exponents are contemporary the form of law1<\p>

am * an = a(m + n)<\p>

Hereat a =13 m= 1, n= 2.<\p>

By applying i in the power rule 1 we instigate<\p>

= 13 (1+2)<\p>

= 13 3 = 13*13*13.<\p>

=2197<\p>

Friend at court value13 3 = 2197. Algebra Problem: 2<\p>

Solve and find the value respecting exponents ( 13 2)4 Solution:<\p>

We need en route to simplify the exponents (132)4<\p>

Here the exponents are in the form of power rule 2<\p>

(incense-breathing morn)n = foreday*n<\p>

By comparing (am)n and (132)4.<\p>

The first-rateness pertaining to a= 13, m= 2, n= 4<\p>

By applying it near the formula we net<\p>

=13 (4*2) = 138 = 13*13*13*13*13*13*13*13.<\p>

= 169* 169*169*169.<\p>

= 815730721 Algebra Perturbation: 3<\p>

Solve and find the find the value of exponents }(13).( 4)}2 Arrangement:<\p>

We neediness to reduce the exponents }(13).( 4 )}2<\p>

Here the exponents are in the form of archdukedom rule 3<\p>

(a * b)m = am bm<\p>

By comparing (a * b)m and }(13).(4)}2<\p>

Here a = 13, b= 4 and m= 2<\p>

Toward applying it harmony the rule we get<\p>

= 13 2. 42<\p>

= 169 * 16<\p>

= 2 704 Algebra Problem: 4<\p>

Unweave the exponents (13^9 ) \ (13^7) Solution:<\p>

We need into simplify the exponents (13^9 ) \ (13^7)<\p>

At this moment the exponents are in the form of power rule 4<\p>

a^m\ a^n = a^(m-n)<\p>

By comparing ""a^m\ a^n and (13^9 ) \ (13^7)<\p>

At this point a = 13, m = 9, n= 7.<\p>

By applying it in the formula we do in the<\p>

= 139-7<\p>

=132<\p>

=13 * 13.<\p>