How do you simplify (5^8)^3(58)3?

2 Answers
Jan 10, 2016

Explanation is given below.

Explanation:

Exponent rules or sometimes called as laws of exponents.
You can go over the rules and would be in a position to solve many such problems as you have shared.

Let us understand exponents in easier manner.

a^1=aa1=a
a^2=a*aa2=aa
a^3=a*a*aa3=aaa

You can see the exponent denotes the number of time the base is to be multiplied with itself.

A very common rule is

a^m*a^n = a^(m+n)aman=am+n

You should be familiar with it, if not take some time and go over the rules it would be such a life saver later on in Maths.

Now let us come problem similar to ours.

Example : (a^2)^3(a2)3

This we can write as a^2*a^2*a^2a2a2a2 that is what we understand by exponents.

Now applying the rule we can see

(a^2)^3 = a^2*a^2*a^2(a2)3=a2a2a2
(a^2)^3 = a^(2+2+2)(a2)3=a2+2+2
(a^2)^3 = a^6(a2)3=a6

Now I would like to point out that the product of the two exponents here that is 22 and 33 also gives us 66

To generalize

(a^m)^n = a^(mxxn)(am)n=am×n

The above rule can be used for our problem.

(5^8)^3(58)3

=5^(8xx3)=58×3

=5^24=524 Answer.

Jan 10, 2016

The answer would be 5^24524, as (x^m)^n=x^(mn)(xm)n=xmn

Explanation:

We understand that raising something to a power produces a product of that number and itself as many times as the number the power is.
e.g. 6^3=6*6*663=666
So (5^8)^3=5^8*5^8*5^8(58)3=585858

By our law of indicies: x^n*x^m=x^(n+m)xnxm=xn+m

We therefore have: (5^8)^3=5^8*5^8*5^8=5^(8+8+8)=5^24(58)3=585858=58+8+8=524

Taking it even simpler, 5^8=5*5*5*5*5*5*5*558=55555555

So: 5^8*5^8*5^8=5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5=5^24585858=555555555555555555555555=524

Overall, the rule is, if you have a number raised to a power, and both the number and power are raised to another power, you can simply multiply the two powers together to get the new power for the number.

e.g: (x^m)^n=x^(mn)(xm)n=xmn