Question

What expression is equivalent to (3^-4y^5)^-2

Answer 1

To simplify the expression \((3^{-4}y^{5})^{-2}\), you can apply the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

Let's apply this to each part of the expression:

1. Apply the exponent to the base \(3^{-4}\):
\[
(3^{-4})^{-2} = 3^{-4 \cdot -2} = 3^{8}
\]

2. Apply the exponent to the variable \(y^5\):
\[
(y^{5})^{-2} = y^{5 \cdot -2} = y^{-10}
\]

Now, combine the results:
\[
(3^{-4}y^{5})^{-2} = 3^{8}y^{-10}
\]

Thus, the expression \((3^{-4}y^5)^{-2}\) is equivalent to:
\[
3^{8}y^{-10}
\]

If required, you can also express \(y^{-10}\) in the denominator:
\[
\frac{3^{8}}{y^{10}}
\]

Therefore, the final equivalent expression is:
\[
3^{8}y^{-10} \quad \text{or} \quad \frac{3^{8}}{y^{10}}
\]