Question(357) $\sqrt[9]{5} ; \sqrt[3]{\frac{8}{3}} ; \sqrt{\frac{3}{2}}$ . $358 \sqrt[6]{2} ; \quad \sqrt[8]{\frac{5}{3}} ; \quad \sqrt[4]{\frac{3}{2}}$ .

Studdy Solution

STEP 1

1. We are tasked with simplifying or comparing the expressions given.
2. The expressions involve roots of different orders, which can be expressed as fractional exponents.
3. We will express each root in terms of fractional exponents for easier comparison or simplification.

STEP 2

1. Convert each root expression to a fractional exponent.
2. Simplify or compare the expressions if needed.

STEP 3

Convert each root expression in Problem 357 to a fractional exponent:
1. $\sqrt[9]{5}$ can be written as $5^{1/9}$ .
2. $\sqrt[3]{\frac{8}{3}}$ can be written as $(\frac{8}{3})^{1/3}$ .
3. $\sqrt{\frac{3}{2}}$ can be written as $(\frac{3}{2})^{1/2}$ .

STEP 4

Convert each root expression in Problem 358 to a fractional exponent:
1. $\sqrt[6]{2}$ can be written as $2^{1/6}$ .
2. $\sqrt[8]{\frac{5}{3}}$ can be written as $(\frac{5}{3})^{1/8}$ .
3. $\sqrt[4]{\frac{3}{2}}$ can be written as $(\frac{3}{2})^{1/4}$ .

STEP 5

If the task is to compare or simplify, we can now use the properties of exponents. However, since the problem does not specify further actions, we have completed the conversion to fractional exponents.
The expressions have been converted to fractional exponents for easier manipulation or comparison: - Problem 357: $5^{1/9}$ , $(\frac{8}{3})^{1/3}$ , $(\frac{3}{2})^{1/2}$ . - Problem 358: $2^{1/6}$ , $(\frac{5}{3})^{1/8}$ , $(\frac{3}{2})^{1/4}$ .

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