Question

When raising a power to another power, how are the exponents simplified?

Answer 1

Hint: When raising a power to another power, we will follow the rule of exponents in which the power of power converts into multiplication. In mathematical form, we can assume an exponent that is $a^n$ . We will raise $m$ power to the power of exponent as ${\left(a^n\right)}^m$ . Now, we can recollect the property for simplifying it.

Complete step-by-step answer:
Since, we have the question in a statement as:
“When raising a power to another power, how are the exponents simplified?”
Here, we can convert this question in mathematical form as:
$\Rightarrow {\left(a^n\right)}^m=?$
Here is the answer of the question that is a statement also:
“When we raise a power to another power, the Power will be multiplied to each other.”
Since, we got the answer also in the form of a statement. Here, we will convert it into mathematical form as:
$\Rightarrow {\left(a^n\right)}^m=a^{n\times m}$
Now, we will try to understand it by a example:
Let, the question is $${\left(5^2\right)}^3$$ .
As we got the answer that the power of the power will be multiplication of power. We will do as:
$$\Rightarrow {\left(5^2\right)}^3$$
$\Rightarrow 5^{2\times 3}$
Now, we will do multiplication of power as:
$\Rightarrow 5^6$
Further, we will simplify the exponent by multiplying it by itself $6$ times as:
$\Rightarrow 5\times 5\times 5\times 5\times 5\times 5$
Now, after multiplying it $6$ times, we will have:
$\Rightarrow 15625$
Hence, the simplified value of $${\left(5^2\right)}^3$$ is $15625$ .

Note: Since, we got the answer of the question in a statement that is:
“When we raise a power to another power, the power will be multiplied to each other.”
Here, we will represent it in mathematical form as:
$\Rightarrow {\left(a^n\right)}^m=a^{n\times m}$
Now, we will check it with the help of the example that we already took in the solution that is:
$$\Rightarrow {\left(5^2\right)}^3$$
Since, we solved it according to the statement of answer of the question but here, we will solve it as it is given step by step. Firstly, we will solve the bracketed term by squaring it as:
$$\Rightarrow {\left(25\right)}^3$$
Now, we will calculate the cube as:
$$\Rightarrow 25\times 25\times 25$$
Now, we will do multiplication and will get:
$$\Rightarrow 15625$$
Since, we got the same answer that means the solution is correct.