Question

8 Which expression is equivalent to (x ^ 9 * y * z ^ 4) ^ 5 ?
Q
H x ^ 45 * y * z ^ 20
x ^ 45 * y ^ 5 * z ^ 20
G x ^ 14 * y ^ 5 * z ^ 9
F x ^ 14 * y ^ 6 * z ^ 9

Answer 1

To simplify the expression \((x^9 * y * z^4)^5\), we can use the power of a product rule, which states that \((a * b * c)^n = a^n * b^n * c^n\).

Applying this to our expression:

\[
(x^9 * y * z^4)^5 = (x^9)^5 * (y)^5 * (z^4)^5
\]

Now we calculate each part:

1. \((x^9)^5 = x^{9 * 5} = x^{45}\)
2. \((y)^5 = y^5\)
3. \((z^4)^5 = z^{4 * 5} = z^{20}\)

Putting it all together, we have:

\[
x^{45} * y^5 * z^{20}
\]

Thus, the expression \((x^9 * y * z^4)^5\) simplifies to:

\[
x^{45} * y^5 * z^{20}
\]

The equivalent expression is:

**\(x^{45} * y^5 * z^{20}\)**

So, the correct answer is:

**x ^ 45 * y ^ 5 * z ^ 20**