Select the equivalent expression. root(21)((1)/(d^(-7)*d)) d^((2)/(7)) d^((7)/(2)) d^(-(7)/(2)) d^(-(2)/(7))

Simplify Inside Radical: Simplify the expression inside the radical. We have the expression root(21)((1)/(d^(-7)*d)). First, we need to simplify the denominator by multiplying d^(-7) by d. Using the property of exponents that states a^(m) * a^(n) = a^(m+n), we get: d^(-7) * d = d^(-7+1) = d^(-6). So, the expression becomes root(21)((1)/(d^(-6))).Move Denominator to Numerator: Simplify the expression further by moving the denominator to the numerator. Using the property of exponents that states (1/a^(-n)) = a^n, we can rewrite the expression as: root(21)(d^6).Convert to Exponent Form: Convert the radical expression to an exponent form. The 21st root of d^6 can be written as d^(6/21). Simplify the fraction 6/21 by dividing both the numerator and the denominator by their greatest common divisor, which is 3. d^(6/21) = d^(2/7).Identify Equivalent Expression: Identify the equivalent expression from the given options. The simplified expression is d^(2/7), which matches one of the given options.

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Select the equivalent expression.

root(21)((1)/(d^(-7)*d))

d^((2)/(7))

d^((7)/(2))

d^(-(7)/(2))

d^(-(2)/(7))

Select the equivalent expression. $\newline$ $\sqrt[21]{\frac{1}{d^{-7} \cdot d}}$ $\newline$ $d^{\frac{2}{7}}$ $\newline$ $d^{\frac{7}{2}}$ $\newline$ $d^{-\frac{7}{2}}$ $\newline$ $d^{-\frac{2}{7}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[21]{\frac{1}{d^{-7} \cdot d}}

\newline

d^{\frac{2}{7}}

\newline

d^{\frac{7}{2}}

\newline

d^{-\frac{7}{2}}

\newline

d^{-\frac{2}{7}}

Simplify Inside Radical: Simplify the expression inside the radical. $\newline$ We have the expression $\sqrt[21]{\frac{1}{d^{-7} \cdot d}}$ . First, we need to simplify the denominator by multiplying $d^{-7}$ by $d$ . $\newline$ Using the property of exponents that states $a^{m} \cdot a^{n} = a^{m+n}$ , we get: $\newline$ $d^{-7} \cdot d = d^{-7+1} = d^{-6}$ . $\newline$ So, the expression becomes $\sqrt[21]{\frac{1}{d^{-6}}}$ .
Move Denominator to Numerator: Simplify the expression further by moving the denominator to the numerator. $\newline$ Using the property of exponents that states $(1/a^{-n}) = a^n$ , we can rewrite the expression as: $\newline$ $\sqrt[21]{d^6}$ .
Convert to Exponent Form: Convert the radical expression to an exponent form. $\newline$ The $21^{\text{st}}$ root of $d^6$ can be written as $d^{(6/21)}$ . $\newline$ Simplify the fraction $6/21$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $\newline$ $d^{(6/21)} = d^{(2/7)}$ .
Identify Equivalent Expression: Identify the equivalent expression from the given options. $\newline$ The simplified expression is $d^{\frac{2}{7}}$ , which matches one of the given options.