Questions: Evaluate the expression without using a calculator. 125^(2/3) Rewrite the expression using a radical. 125^(2/3)=( Do not evaluate.)

Solution Steps

The expression $125^{\frac{2}{3}}$ can be rewritten using radicals. Recall that $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. Applying this rule: $$125^{\frac{2}{3}} = \sqrt[3]{125^2}$$

First, calculate $125^2$: $$125^2 = 125 \times 125 = 15625$$ So, the expression becomes: $$\sqrt[3]{15625}$$

Now, evaluate $\sqrt[3]{15625}$. Since $25^3 = 15625$, the cube root of 15625 is 25. Thus: $$\sqrt[3]{15625} = 25$$

The expression $125^{\frac{2}{3}}$ can be rewritten as: $$125^{\frac{2}{3}} = \sqrt[3]{125^2}$$

Final Answer