Question

Simplify: (5x^4)^2(1 point)
Responses

10x^8
10 x to the 8th power

5x^6
5 x to the 6th power

25x^6
25 x to the 6th power

25x^8
25 x to the 8th power

Answer 1

To simplify the expression \((5x^4)^2\), you can apply the power of a product rule, which states that \((ab)^n = a^n \cdot b^n\).

So, we can break it down as follows:

\[
(5x^4)^2 = 5^2 \cdot (x^4)^2
\]

Calculating each part:

\[
5^2 = 25
\]

And for \((x^4)^2\), you use the power of a power rule:

\[
(x^4)^2 = x^{4 \cdot 2} = x^8
\]

Putting it all together:

\[
(5x^4)^2 = 25 \cdot x^8 = 25x^8
\]

Thus, the simplified expression is:

**25x^8** (or "25 x to the 8th power")