Question
2. Rewrite each expression in radical form and then evaluate. [2 m a) 121^(1)/(2)= b) (-32)^(3)/(5)=
Solution
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XavierProfessional · Tutor for 6 years
Answer
### a) 11<br />### b) -8
Explain
## Step 1: Rewrite $121^{\frac{1}{2}}$ in radical form<br />### The expression $a^{\frac{1}{n}}$ is equivalent to $\sqrt[n]{a}$. Therefore, $121^{\frac{1}{2}} = \sqrt{121}$.<br /><br />## Step 2: Evaluate $121^{\frac{1}{2}}$<br />### $\sqrt{121} = 11$ since $11 \times 11 = 121$.<br /><br />## Step 3: Rewrite $(-32)^{\frac{3}{5}}$ in radical form<br />### The expression $a^{\frac{m}{n}}$ is equivalent to $(\sqrt[n]{a})^m$. Therefore, $(-32)^{\frac{3}{5}} = (\sqrt[5]{-32})^3$.<br /><br />## Step 4: Evaluate $(-32)^{\frac{3}{5}}$<br />### $\sqrt[5]{-32} = -2$ since $(-2)^5 = -32$. Then, $(-2)^3 = -8$.
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