How do you simplify #(5^8)^3#?
Explanation is given below.
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.
You can see the exponent denotes the number of time the base is to be multiplied with itself.
A very common rule is
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.
This we can write as
Now applying the rule we can see
Now I would like to point out that the product of the two exponents here that is
The above rule can be used for our problem.
The answer would be
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.
By our law of indicies:
We therefore have:
Taking it even simpler,
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.