Question

Which expressions are equivalent to R16? Check all that apply.

Answer 1

Option C:  $(6^{-4})^{-4}$

Option D:  $(6^{-2})^{-8}$

Option F:  $(6^8)^2$

Solution:

Given expression: $6^{16}$

To find which expression is equivalent to the given expression.

Let us solve this using exponent rule: $\left(a^{b}\right)^{c}=a^{b c}$

Option A: $(6^{0})^{16}$

$(6^{0})^{16}=6^{0 \times 16}= 6^0$

It is not equivalent expression.

Option B: $(6^8)^8$

$(6^{8})^{8}=6^{8 \times 8}= 6^{64}$

It is not equivalent expression.

Option C:  $(6^{-4})^{-4}$

$(6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}$

It is equivalent expression for the given expression.

Option D:  $(6^{-2})^{-8}$

$(6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}$

It is equivalent expression for the given expression.

Option E:  $(6^{-1})^{16}$

$(6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}$

It is not equivalent expression.

Option F:  $(6^8)^2$

$(6^{8})^{2}=6^{8 \times 2}= 6^{16}$

It is equivalent expression for the given expression.

Hence $(6^{-4})^{-4}, \ (6^{-2})^{-8}, \ (6^8)^2$ are the equivalent expressions.

Option C, Option D and Option F are correct answers.