Question

Choose the correct word/answer and fill in the blanks:

${\left(4^3\right)}^2$ and ${\left(4^2\right)}^3$ are _________ (same/different)

Answer 1

By the properties of exponent, we know that -

${\left(a^x\right)}^y=a^{x\times y}$

By using the above property -

$$\begin{gathered} {\left(4^3\right)}^2=4^{3\times 2} \\ =4^6 \\ {\left(4^2\right)}^3=4^{2\times 3} \\ =4^6 \end{gathered}$$

Since, ${\left(4^3\right)}^2$ and ${\left(4^2\right)}^3$ are having same exponent and base,

so they will have the same value,

therefore, the correct answer is same.