Question
Express (5y)^4/3
in radical form.
in radical form.
Answers
GPT-4o mini
To express \((5y)^{\frac{4}{3}}\) in radical form, you can follow these steps:
1. Recognize that the expression involves a fractional exponent \(\frac{4}{3}\). The numerator \(4\) indicates a power and the denominator \(3\) indicates a root.
2. Rewrite the expression using radical notation. The expression \((a^m)^{\frac{n}{p}}\) can be expressed as \(\sqrt[p]{(a^m)^n}\).
Thus, we have:
\[
(5y)^{\frac{4}{3}} = \sqrt[3]{(5y)^4}
\]
3. Now compute \((5y)^4\):
\[
(5y)^4 = 5^4 \cdot y^4 = 625y^4
\]
4. Finally, put it all together:
\[
(5y)^{\frac{4}{3}} = \sqrt[3]{625y^4}
\]
Therefore, the expression in radical form is:
\[
\sqrt[3]{625y^4}
\]
1. Recognize that the expression involves a fractional exponent \(\frac{4}{3}\). The numerator \(4\) indicates a power and the denominator \(3\) indicates a root.
2. Rewrite the expression using radical notation. The expression \((a^m)^{\frac{n}{p}}\) can be expressed as \(\sqrt[p]{(a^m)^n}\).
Thus, we have:
\[
(5y)^{\frac{4}{3}} = \sqrt[3]{(5y)^4}
\]
3. Now compute \((5y)^4\):
\[
(5y)^4 = 5^4 \cdot y^4 = 625y^4
\]
4. Finally, put it all together:
\[
(5y)^{\frac{4}{3}} = \sqrt[3]{625y^4}
\]
Therefore, the expression in radical form is:
\[
\sqrt[3]{625y^4}
\]