How do you simplify (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.

a1=a
a2=aa
a3=aaa

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

A very common rule is

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 : (a2)3

This we can write as a2a2a2 that is what we understand by exponents.

Now applying the rule we can see

(a2)3=a2a2a2
(a2)3=a2+2+2
(a2)3=a6

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

(am)n=am×n

The above rule can be used for our problem.

(58)3

=58×3

=524 Answer.

Jan 10, 2016

The answer would be 524, as (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. 63=666
So (58)3=585858

By our law of indicies: xnxm=xn+m

We therefore have: (58)3=585858=58+8+8=524

Taking it even simpler, 58=55555555

So: 585858=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: (xm)n=xmn