Question

Use the power rule and the power of a product rule to simplify the expression.(6n^5)^2

Answer 1

We are giving the expression below and asked to simply

$(6n^5)^2$

We can use the product rule, this formula tells us that when a product is raised to a power, every factor of the product is raised to the power.

We obey the product rule and the above expression becomes

$6^2\times(n^5)^2$

We then use the power rule. This formula tells us that when a power of a number is raised to another power, multiply the indices. This would then give,

$\begin{gathered} 36\times n^{5\times2} \\ =36n^{10} \end{gathered}$

Therefore, the simplified expression gives:

ANSWER

$36n^{10}$