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Determine whether each expression is equivalent to
x^((5)/(3)). Select Yes or No for each expression.
a.
sqrtx No
b.
root(3)(x^(5)) Yes
c.
root(5)(x^(3)) No
d.
sqrt(x^((5)/(3))) No

$3$ . Determine whether each expression is equivalent to $x^{\frac{5}{3}}$ . Select Yes or No for each expression. $\newline$ a. $\sqrt{x}$ No $\newline$ b. $\sqrt[3]{x^{5}}$ Yes $\newline$ c. $\sqrt[5]{x^{3}}$ No $\newline$ d. $\sqrt{x^{\frac{5}{3}}}$ No

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Simplify radical expressions with variables II

Full solution

Q.

3

. Determine whether each expression is equivalent to

x^{\frac{5}{3}}

. Select Yes or No for each expression.

\newline

a.

\sqrt{x}

No

\newline

b.

\sqrt[3]{x^{5}}

Yes

\newline

c.

\sqrt[5]{x^{3}}

No

\newline

d.

\sqrt{x^{\frac{5}{3}}}

No

Compare Exponents: a. $\sqrt{x} = x^{\frac{1}{2}}$ $\newline$ Compare $x^{\frac{1}{2}}$ with $x^{\frac{5}{3}}$ . Since the exponents are different, they are not equivalent.
Equivalent Exponents: b. $\sqrt[3]{x^{5}} = x^{\frac{5}{3}}$ Compare $x^{\frac{5}{3}}$ with $x^{\frac{5}{3}}$ . Since the exponents are the same, they are equivalent.
Compare Exponents: c. $\sqrt[5]{x^{3}} = x^{\frac{3}{5}}$ $\newline$ Compare $x^{\frac{3}{5}}$ with $x^{\frac{5}{3}}$ . Since the exponents are different, they are not equivalent.
Compare Exponents: $d. \sqrt{x^{(5/3)}} = (x^{5/3})^{1/2} = x^{5/6}$ Compare $x^{5/6}$ with $x^{5/3}$ . Since the exponents are different, they are not equivalent.

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