Question

How do you simplify \[{\left( {{x^4}} \right)^5}\]?

Answer 1

Hint: In the given question, we have been given an algebraic expression. In the expression, the variable is raised to a power. This whole expression of the variable being raised to a power is raised to another power. We have to simplify the value of this expression. It can be easily done if we know the identity of a product of powers.

Formula Used:
We are going to use the product of powers formula, which is,
\[{\left( {{a^m}} \right)^n} = {a^{m \times n}}\]

Complete step by step answer:
The given expression is \[{\left( {{x^4}} \right)^5}\].
To solve it, we are going to use the product of powers formula, which is,
\[{\left( {{a^m}} \right)^n} = {a^{m \times n}}\]

Hence, \[{\left( {{x^4}} \right)^5} = {x^{4 \times 5}} = {x^{20}}\]

Note:
In the given question we were given an algebraic expression. In it, a variable was raised to a power which again was raised to another power. We had to solve it. We did that by using the identity of a product of powers. So, it is important that we know the identities and where to use them.