Question

Rational exponent solve (y ^3/5) ^10/15

Answer 1

To solve \((y^{\frac{3}{5}})^{\frac{10}{15}}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).

Here, we have:

\[
(y^{\frac{3}{5}})^{\frac{10}{15}} = y^{\frac{3}{5} \cdot \frac{10}{15}}
\]

Next, we simplify \(\frac{10}{15}\):

\[
\frac{10}{15} = \frac{2}{3}
\]

Now we multiply the exponents:

\[
\frac{3}{5} \cdot \frac{2}{3} = \frac{3 \cdot 2}{5 \cdot 3} = \frac{6}{15}
\]

So, our expression simplifies to:

\[
y^{\frac{6}{15}}
\]

Lastly, we can simplify \(\frac{6}{15}\):

\[
\frac{6}{15} = \frac{2}{5}
\]

Thus, the final result is:

\[
y^{\frac{2}{5}}
\]