Question

Write each expression in radical form. 7^(1)/(2) 2^(5)/(3) 6^(3)/(2)cdot 2^(1)/(6) Write each expression in exponential form. (sqrt [4](2))^5 sqrt [6](2) (sqrt [4](5))^5 Simplify. 9^(1)/(2) 36^(3)/(2) 343^-(4)/(3) 1000000^(1)/(6)

Solution

Expert Verified

4.1(202 Voting)

AdrianProfessional · Tutor for 6 years

Answer

### Radical Form: - $7^{\frac {1}{2}} = \sqrt{7}$ - $2^{\frac {5}{3}} = \sqrt[3]{2^5} = \sqrt[3]{32}$ - $6^{\frac {3}{2}}\cdot 2^{\frac {1}{6}} = \sqrt{6^3} \cdot \sqrt[6]{2} = 6\sqrt{6} \cdot \sqrt[6]{2}$ ### Exponential Form: - $(\sqrt [4]{2})^{5} = 2^{\frac{5}{4}}$ - $\sqrt [6]{2} = 2^{\frac{1}{6}}$ - $(\sqrt [4]{5})^{5} = 5^{\frac{5}{4}}$ ### Simplified Values: - $9^{\frac {1}{2}} = \sqrt{9} = 3$ - $36^{\frac {3}{2}} = (36^{\frac{1}{2}})^3 = 6^3 = 216$ - $343^{-\frac {4}{3}} = \frac{1}{(343^{\frac{1}{3}})^4} = \frac{1}{7^4} = \frac{1}{2401}$ - $1000000^{\frac {1}{6}} = \sqrt[6]{1000000} = 10$

Explain

## Step1: Convert to Radical Form ### To convert an expression from exponential form $a^{\frac{m}{n}}$ to radical form, use the identity $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. Apply this to each given expression. ## Step2: Convert to Exponential Form ### To convert a radical expression $(\sqrt[n]{a})^m$ to exponential form, use the identity $(\sqrt[n]{a})^m = a^{\frac{m}{n}}$. Apply this to each given expression. ## Step3: Simplify Expressions ### Simplify each expression by evaluating the power or root as necessary. For example, $a^{\frac{1}{2}}$ is the square root of $a$, and $a^{-\frac{m}{n}}$ is the reciprocal of $\sqrt[n]{a^m}$.

Click to rate: