Solve for x cube root of x=3 cube root of 7

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

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

${\sqrt[3]{x}}^{3} = {(3 \sqrt[3]{7})}^{3}$

Simplify each side of the equation.

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

${(x^{\frac{1}{3}})}^{3} = {(3 \sqrt[3]{7})}^{3}$

Simplify the left side.

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

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

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

$x^{\frac{1}{3} \cdot 3} = {(3 \sqrt[3]{7})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = {(3 \sqrt[3]{7})}^{3}$

Rewrite the expression.

$x^{1} = {(3 \sqrt[3]{7})}^{3}$

Simplify.

$x = {(3 \sqrt[3]{7})}^{3}$

Simplify the right side.

Simplify ${(3 \sqrt[3]{7})}^{3}$ .

Simplify the expression.

Apply the product rule to $3 \sqrt[3]{7}$ .

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

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

$x = 27 {\sqrt[3]{7}}^{3}$

Rewrite ${\sqrt[3]{7}}^{3}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7}$ as $7^{\frac{1}{3}}$ .

$x = 27 {(7^{\frac{1}{3}})}^{3}$

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

$x = 27 \cdot 7^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$x = 27 \cdot 7^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = 27 \cdot 7^{\frac{3}{3}}$

Rewrite the expression.

$x = 27 \cdot 7^{1}$

Evaluate the exponent.

$x = 27 \cdot 7$

Multiply $27$ by $7$ .

$x = 189$