Question

select all the expressions that are equivalent to $\frac{3^{14}}{3^{2}}$.
$(3^{4})^{3}$ $3^{7}$ $3^{16}$ $\frac{1}{3^{7}}$

Explanation:

Step1: Simplify the given expression

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$
$\frac{3^{14}}{3^2}=3^{14-2}=3^{12}$

Step2: Evaluate each option

Option1: $(3^4)^3$

Use exponent rule $(a^m)^n=a^{m \times n}$
$(3^4)^3=3^{4 \times 3}=3^{12}$

Option2: $3^7$

This equals $3^7$, which is not $3^{12}$

Option3: $3^{16}$

This equals $3^{16}$, which is not $3^{12}$

Option4: $\frac{1}{3^7}$

This equals $3^{-7}$, which is not $3^{12}$

Answer:

A. $(3^4)^3$