Select the equivalent expression. root(15)((h^(4))/(h^(-5))) h^(-(5)/(3)) h^((5)/(3)) h^(-(3)/(5)) h^((3)/(5))

Simplify Exponent Inside Radical: Simplify the expression inside the radical. We have the expression root(15)((h^(4))/(h^(-5))). To simplify, we use the property of exponents that states when dividing like bases, we subtract the exponents. So, (h^(4))/(h^(-5)) = h^(4 - (-5)) = h^(4 + 5) = h^(9).Apply 15th Root: Apply the 15th root to the simplified expression. Now we apply the 15th root to h^(9), which can be written as (h^(9))^(1/15). Using the property of exponents (a^(m))^n = a^(m*n), we get h^(9*(1/15)) = h^(9/15).Simplify Exponent: Simplify the exponent. Simplify the fraction 9/15 by dividing both the numerator and the denominator by their greatest common divisor, which is 3. h^(9/15) = h^(3/5).Match with Options: Match the simplified expression with the given options. The simplified expression is h^(3/5), which matches one of the given options.

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Select the equivalent expression.

root(15)((h^(4))/(h^(-5)))

h^(-(5)/(3))

h^((5)/(3))

h^(-(3)/(5))

h^((3)/(5))

Select the equivalent expression. $\newline$ $\sqrt[15]{\frac{h^{4}}{h^{-5}}}$ $\newline$ $h^{-\frac{5}{3}}$ $\newline$ $h^{\frac{5}{3}}$ $\newline$ $h^{-\frac{3}{5}}$ $\newline$ $h^{\frac{3}{5}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[15]{\frac{h^{4}}{h^{-5}}}

\newline

h^{-\frac{5}{3}}

\newline

h^{\frac{5}{3}}

\newline

h^{-\frac{3}{5}}

\newline

h^{\frac{3}{5}}

Simplify Exponent Inside Radical: Simplify the expression inside the radical. $\newline$ We have the expression $\sqrt[15]{\left(\frac{h^{4}}{h^{-5}}\right)}$ . To simplify, we use the property of exponents that states when dividing like bases, we subtract the exponents. $\newline$ So, $\frac{h^{4}}{h^{-5}} = h^{4 - (-5)} = h^{4 + 5} = h^{9}$ .
Apply $15$ th Root: Apply the $15$ th root to the simplified expression. $\newline$ Now we apply the $15$ th root to $h^{9}$ , which can be written as $(h^{9})^{\frac{1}{15}}$ . $\newline$ Using the property of exponents $(a^{m})^{n} = a^{m*n}$ , we get $h^{9*\frac{1}{15}} = h^{\frac{9}{15}}$ .
Simplify Exponent: Simplify the exponent. $\newline$ Simplify the fraction $\frac{9}{15}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $\newline$ $h^{\frac{9}{15}} = h^{\frac{3}{5}}$ .
Match with Options: Match the simplified expression with the given options. $\newline$ The simplified expression is $h^{\frac{3}{5}}$ , which matches one of the given options.