Given x > 0, the expression root(8)(x^(73)) is equivalent to x^(9)root(8)(x^(2)) x^(10root(8)(x^(2))) x^(10)root(8)(x) x^(9)root(8)(x)

Understand Expression and Properties: Understand the given expression and the properties of exponents. The given expression is root(8)(x^(73)), which means we are looking for the 8th root of x raised to the 73rd power. According to the properties of exponents, we can rewrite the expression as x^(73/8).Simplify Exponent Division: Simplify the exponent by dividing 73 by 8. When we divide 73 by 8, we get 9 with a remainder of 1. This means that x^(73/8) can be written as x^(9 + 1/8).Separate Whole and Fractional Exponents: Separate the whole number exponent from the fractional exponent. We can rewrite x^(9 + 1/8) as x^9 * x^(1/8). This separates the whole number exponent from the fractional exponent, which represents the 8th root of x.Recognize 8th Root of x: Recognize that x^(1/8) is the 8th root of x. The expression x^(1/8) is equivalent to the 8th root of x, which can be written as root(8)(x).Combine Expressions for Final Result: Combine the expressions to form the final equivalent expression. The final equivalent expression is x^9 * root(8)(x), which is one of the given options.

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Given
x > 0, the expression
root(8)(x^(73)) is equivalent to

x^(9)root(8)(x^(2))

x^(10root(8)(x^(2)))

x^(10)root(8)(x)

x^(9)root(8)(x)

Given x>0 , the expression $\sqrt[8]{x^{73}}$ is equivalent to $\newline$ $x^{9} \sqrt[8]{x^{2}}$ $\newline$ $x^{10 \sqrt[8]{x^{2}}}$ $\newline$ $x^{10} \sqrt[8]{x}$ $\newline$ $x^{9} \sqrt[8]{x}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Given

x>0

, the expression

\sqrt[8]{x^{73}}

is equivalent to

\newline

x^{9} \sqrt[8]{x^{2}}

\newline

x^{10 \sqrt[8]{x^{2}}}

\newline

x^{10} \sqrt[8]{x}

\newline

x^{9} \sqrt[8]{x}

Understand Expression and Properties: Understand the given expression and the properties of exponents. $\newline$ The given expression is $\sqrt[8]{x^{73}}$ , which means we are looking for the $8^{\text{th}}$ root of $x$ raised to the $73^{\text{rd}}$ power. According to the properties of exponents, we can rewrite the expression as $x^{\frac{73}{8}}$ .
Simplify Exponent Division: Simplify the exponent by dividing $73$ by $8$ . When we divide $73$ by $8$ , we get $9$ with a remainder of $1$ . This means that $x^{(73/8)}$ can be written as $x^{(9 + 1/8)}$ .
Separate Whole and Fractional Exponents: Separate the whole number exponent from the fractional exponent. $\newline$ We can rewrite $x^{9 + \frac{1}{8}}$ as $x^9 \cdot x^{\frac{1}{8}}$ . This separates the whole number exponent from the fractional exponent, which represents the $8$ th root of $x$ .
Recognize $8$ th Root of $x$ : Recognize that $x^{\frac{1}{8}}$ is the $8$ th root of $x$ . The expression $x^{\frac{1}{8}}$ is equivalent to the $8$ th root of $x$ , which can be written as $\sqrt[8]{x}$ .
Combine Expressions for Final Result: Combine the expressions to form the final equivalent expression. $\newline$ The final equivalent expression is $x^9 \cdot \sqrt[8]{x}$ , which is one of the given options.