Which of the following equivalent to (1/8)^4?

Which of the following equivalent to (1/8)^4?

$$\left(A\right)\ \left(0.5\right)^5$$
$$\left(B\right)\ \left(0.25\right)^3$$
$$\left(C\right)\ \left(0.25\right)^6$$
$$\left(D\right)\ \left(0.4\right)^3$$
$$\left(E\right)\ \left(0.8\right)^2$$

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Hi AAPL,
Let's take a look at your question.

We will first write the given expression in its simplest form.
$$\left(\frac{1}{8}\right)^{^4}=\left(\frac{1}{2\times2\times2}\right)^{^4}$$
$$ =\left(\frac{1}{2^3}\right)^{^4}=\left(\frac{1}{2}\right)^{^{12}}$$

Now we will check which of the given options is equivalent to the expression above.

OPTION A:
$$\left(0.5\right)^{^5}$$
$$=\left(\frac{5}{10}\right)^{^5}=\left(\frac{1}{2}\right)^{^5}\ne\left(\frac{1}{2}\right)^{^{12}}$$

OPTION B:
$$\left(0.25\right)^{^3}$$
$$=\left(\frac{25}{100}\right)^{^3}=\left(\frac{1}{4}\right)^{^3}=\left(\frac{1}{2^2}\right)^{^3}=\left(\frac{1}{2}\right)^{^6}\ne\left(\frac{1}{2}\right)^{^{12}}$$

OPTION C:
$$\left(0.25\right)^{^6}$$
$$=\left(\frac{25}{100}\right)^{^6}=\left(\frac{1}{4}\right)^{^6}=\left(\frac{1}{2^2}\right)^{^6}=\left(\frac{1}{2}\right)^{^{12}}$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.