Evaluate the Expression: Finding the Value of 8^(-2x)

$8^{-2x}=\text{?}$

Let's use the law of exponents for negative exponents:

$a^{-n}=\frac{1}{a^n}$and apply it to our problem:

$$$$$8^{-2x}=\frac{1}{8^{2x}}$Next, we'll use the law of exponents for power of a power:

$(a^m)^n=a^{m\cdot n}$and apply this law to the denominator in the expression we got:

$\frac{1}{8^{2x}}=\frac{1}{(8^2)^x}=\frac{1}{64^x}$where we actually used the above law in the opposite direction, meaning instead of expanding the parentheses and multiplying by the power exponent, we interpreted the multiplication by the power exponent as a power of a power, and in the final stage we calculated the power inside the parentheses in the denominator.

Let's summarize the solution steps, we got that:

$8^{-2x}= \frac{1}{8^{2x}}=\frac{1}{64^x}$

Therefore, the correct answer is answer D.