Select the equivalent expression. root(24)((1)/(x*x^(5))) x^(-(1)/(4)) x^((1)/(4)) x^(4) x^(-4)

Understand the expression: Understand the given expression. We need to simplify the expression root(24)((1)/(x*x^(5))). This involves a 24th root and a division of exponents.Simplify inside the root: Simplify the expression inside the root. The expression inside the root is (1)/(x*x^(5)). Combine the exponents by adding them since the bases are the same and we are dividing. (1)/(x^(1+5)) = (1)/(x^6)Apply root to expression: Apply the root to the simplified expression. Now we take the 24th root of (1)/(x^6). root(24)((1)/(x^6)) Since taking the root is the same as raising to the power of 1/24, we can rewrite this as: (1/x^6)^(1/24)Apply exponent rule: Apply the exponent rule (a^(m/n) = (a^m)^(1/n)). We can apply the exponent rule to the expression. (1^(1/24))/(x^(6*(1/24))) Since 1 raised to any power is 1, we can simplify the numerator to 1. 1/(x^(6/24))Simplify denominator exponent: Simplify the exponent in the denominator. Simplify the fraction 6/24 to its lowest terms. 6/24 = 1/4 So, the expression becomes: 1/(x^(1/4))Rewrite as negative exponent: Rewrite the expression as a negative exponent. Since 1/(x^(1/4)) is the same as x^(-1/4), we can rewrite the expression as: x^(-(1/4))

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Select the equivalent expression.

root(24)((1)/(x*x^(5)))

x^(-(1)/(4))

x^((1)/(4))

x^(4)

x^(-4)

Select the equivalent expression. $\newline$ $\sqrt[24]{\frac{1}{x \cdot x^{5}}}$ $\newline$ $x^{-\frac{1}{4}}$ $\newline$ $x^{\frac{1}{4}}$ $\newline$ $x^{4}$ $\newline$ $x^{-4}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\sqrt[24]{\frac{1}{x \cdot x^{5}}}

\newline

x^{-\frac{1}{4}}

\newline

x^{\frac{1}{4}}

\newline

x^{4}

\newline

x^{-4}

Understand the expression: Understand the given expression. $\newline$ We need to simplify the expression $\sqrt[24]{\frac{1}{x*x^{5}}}$ . $\newline$ This involves a $24^{\text{th}}$ root and a division of exponents.
Simplify inside the root: Simplify the expression inside the root. $\newline$ The expression inside the root is $(1)/(x\cdot x^{5})$ . $\newline$ Combine the exponents by adding them since the bases are the same and we are dividing. $\newline$ $(1)/(x^{1+5})$ $\newline$ = $(1)/(x^{6})$
Apply root to expression: Apply the root to the simplified expression. $\newline$ Now we take the $24^{\text{th}}$ root of $(1)/(x^6)$ . $\newline$ $\sqrt[24]{\frac{1}{x^6}}$ $\newline$ Since taking the root is the same as raising to the power of $1/24$ , we can rewrite this as: $\newline$ $(\frac{1}{x^6})^{\frac{1}{24}}$
Apply exponent rule: Apply the exponent rule $a^{\frac{m}{n}} = (a^m)^{\frac{1}{n}}$ . We can apply the exponent rule to the expression. $\frac{1^{\frac{1}{24}}}{x^{6\cdot(\frac{1}{24})}}$ Since $1$ raised to any power is $1$ , we can simplify the numerator to $1$ . $\frac{1}{x^{\frac{6}{24}}}$
Simplify denominator exponent: Simplify the exponent in the denominator. $\newline$ Simplify the fraction $\frac{6}{24}$ to its lowest terms. $\newline$ $\frac{6}{24} = \frac{1}{4}$ $\newline$ So, the expression becomes: $\newline$ $\frac{1}{x^{\frac{1}{4}}}$
Rewrite as negative exponent: Rewrite the expression as a negative exponent. $\newline$ Since $1/(x^{1/4})$ is the same as $x^{-1/4}$ , we can rewrite the expression as: $\newline$ $x^{-(1/4)}$