$$
\sqrt[3]{70 n}(\sqrt[4]{70 n})^{2}
$$

For what value of $x$ is the given expression equivalent to $(70 n)^{20 x}$, where $n1$ ?

Question

$$
\sqrt[3]{70 n}(\sqrt[4]{70 n})^{2}
$$

For what value of $x$ is the given expression equivalent to $(70 n)^{20 x}$, where $n>1$ ?

StudyXY · Accepted Answer

: Recognize that the given expression is a cube root and a fourth power multiplied together. : To make the base of both radicals the same, we can rewrite the fourth root as a cube root and a remaining fourth power. : Simplify the expression further. : We want the exponent of $70 n$ to be $20x$. : Since we want the entire expression to be equal to $(70 n)^{20x}$, the exponents on the left side of the equation should be equal to the exponent on the right side of the equation. : Solve for $x$. The given expression is equivalent to $(70 n)^{20x}$ when $x = \boxed{\frac{1}{24}}$.

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QuestionAnatomy and Physiology

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Step 1
: Recognize that the given expression is a cube root and a fourth power multiplied together.

Step 2
: To make the base of both radicals the same, we can rewrite the fourth root as a cube root and a remaining fourth power.

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