Question
rational exponent of ^3√125
Answers
GPT-4o mini
To express \( \sqrt[3]{125} \) with a rational exponent, you can convert the cube root into exponent form:
\[
\sqrt[3]{125} = 125^{1/3}
\]
Next, since \( 125 = 5^3 \), you can substitute that into the expression:
\[
125^{1/3} = (5^3)^{1/3}
\]
Using the power of a power property, you multiply the exponents:
\[
(5^3)^{1/3} = 5^{3 \cdot \frac{1}{3}} = 5^1 = 5
\]
So, \( \sqrt[3]{125} \) can be expressed as both \( 125^{1/3} \) and evaluates to 5.
\[
\sqrt[3]{125} = 125^{1/3}
\]
Next, since \( 125 = 5^3 \), you can substitute that into the expression:
\[
125^{1/3} = (5^3)^{1/3}
\]
Using the power of a power property, you multiply the exponents:
\[
(5^3)^{1/3} = 5^{3 \cdot \frac{1}{3}} = 5^1 = 5
\]
So, \( \sqrt[3]{125} \) can be expressed as both \( 125^{1/3} \) and evaluates to 5.