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

Given Expression: We are given the expression root(8)(x^(9)) and we need to simplify it. The 8th root of x to the 9th power can be expressed as x^(9/8).Separate into Parts: We can separate x^(9/8) into two parts: x^(8/8) * x^(1/8). This is because 9/8 can be divided into 1 (which is 8/8) plus 1/8.Simplify x^(8/8): Simplify x^(8/8) to x^1, because any non-zero number to the power of 1 is the number itself. So we have x * x^(1/8).Rewrite x^(1/8): Now we can rewrite x^(1/8) as the 8th root of x, which gives us the final expression: x * root(8)(x).

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

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

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

xroot(8)(x)

xroot(8)(x^(2))

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Given

x>0

, the expression

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

is equivalent to

\newline

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

\newline

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

\newline

x \sqrt[8]{x}

\newline

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

Given Expression: We are given the expression $\sqrt[8]{x^{9}}$ and we need to simplify it. The $8$ th root of $x$ to the $9$ th power can be expressed as $x^{\frac{9}{8}}$ .
Separate into Parts: We can separate $x^{\frac{9}{8}}$ into two parts: $x^{\frac{8}{8}} \times x^{\frac{1}{8}}$ . This is because $\frac{9}{8}$ can be divided into $1$ (which is $\frac{8}{8}$ ) plus $\frac{1}{8}$ .
Simplify $x^{\frac{8}{8}}$ : Simplify $x^{\frac{8}{8}}$ to $x^1$ , because any non-zero number to the power of $1$ is the number itself. So we have $x \cdot x^{\frac{1}{8}}$ .
Rewrite $x^{\frac{1}{8}}$ : Now we can rewrite $x^{\frac{1}{8}}$ as the $8$ th root of $x$ , which gives us the final expression: $x \cdot \sqrt[8]{x}$ .