Question

Which expression is equivalent to (64 y Superscript 100 Baseline) Superscript one-half?
8y10
8y50
32y10
32y50

Answer 1

To simplify the expression \((64y^{100})^{1/2}\), we can apply the exponent rule, which states that \((a^m)^{n} = a^{m \cdot n}\).

1. First, split the expression into the separate components:
\[
(64)^{1/2} \cdot (y^{100})^{1/2}
\]

2. Calculate \((64)^{1/2}\):
\[
(64)^{1/2} = \sqrt{64} = 8
\]

3. Calculate \((y^{100})^{1/2}\):
\[
(y^{100})^{1/2} = y^{100 \cdot \frac{1}{2}} = y^{50}
\]

4. Combine the two results:
\[
8 \cdot y^{50} = 8y^{50}
\]

Thus, the expression \((64y^{100})^{1/2}\) simplifies to \(8y^{50}\).

So the equivalent expression is **8y⁵⁰**.