Solve for r r^(4/7)=16

$r^{\frac{4}{7}} = 16$

Raise each side of the equation to the $\frac{7}{4}$ power to eliminate the fractional exponent on the left side.

${(r^{\frac{4}{7}})}^{\frac{7}{4}} = \pm {(16)}^{\frac{7}{4}}$

Solve the equation for $r$ .

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Simplify the right side of the equation.

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Simplify the expression.

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Rewrite $16$ as $2^{4}$ .

$r = \pm {(2^{4})}^{\frac{7}{4}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$r = \pm 2^{4 (\frac{7}{4})}$

Cancel the common factor of $4$ .

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Cancel the common factor.

$r = \pm 2^{4 (\frac{7}{4})}$

Rewrite the expression.

$r = \pm 2^{7}$

Raise $2$ to the power of $7$ .

$r = \pm 128$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$r = 128$

Next, use the negative value of the $\pm$ to find the second solution.

$r = - 128$

The complete solution is the result of both the positive and negative portions of the solution.

$r = 128, - 128$

Solve for r r^(4/7)=16

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