How do you simplify (5^8)^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=a
a^2=a*a
a^3=a*a*a

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)

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

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

Now applying the rule we can see

(a^2)^3 = a^2*a^2*a^2
(a^2)^3 = a^(2+2+2)
(a^2)^3 = a^6

Now I would like to point out that the product of the two exponents here that is 2 and 3 also gives us 6

To generalize

(a^m)^n = a^(mxxn)

The above rule can be used for our problem.

(5^8)^3

=5^(8xx3)

=5^24 Answer.

Jan 10, 2016

The answer would be 5^24, as (x^m)^n=x^(mn)

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*6
So (5^8)^3=5^8*5^8*5^8

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

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

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

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=5^24

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)