Question

select all the expressions that are equivalent to $(4^{6})^{5}$. the options are $4^{11}$, $4^{30}$, $\frac{1}{4^{11}}$, $\frac{1}{4^{-30}}$

Explanation:

Step1: Apply exponent power rule

$(a^m)^n = a^{m \times n}$
$(4^6)^5 = 4^{6 \times 5} = 4^{30}$

Step2: Compare with options

$4^{11}
eq 4^{30}$, $\frac{1}{4^{11}}
eq 4^{30}$, $\frac{1}{4^{30}}
eq 4^{30}$
Only $4^{30}$ is equivalent, so the selected options (including $4^{11}$, $\frac{1}{4^{11}}$, $\frac{1}{4^{30}}$) are incorrect.

Answer:

None of the selected options are correct. The correct equivalent expression is $4^{30}$.