Solve for a cube root of a=7

$\sqrt[3]{a} = 7$

Step 1

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{a}}^{3} = 7^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{a}$ as $a^{\frac{1}{3}}$ .

${(a^{\frac{1}{3}})}^{3} = 7^{3}$

Simplify the left side.

Simplify ${(a^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${(a^{\frac{1}{3}})}^{3}$ .

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

$a^{\frac{1}{3} \cdot 3} = 7^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$a^{\frac{1}{3} \cdot 3} = 7^{3}$

Rewrite the expression.

$a^{1} = 7^{3}$

Simplify.

$a = 7^{3}$

Simplify the right side.

Raise $7$ to the power of $3$ .

$a = 343$