Solve by Factoring cube root of 21x=-3

$\sqrt[3]{21 x} = - 3$

Step 1

Add $3$ to both sides of the equation.

$\sqrt[3]{21 x} + 3 = 0$

Step 2

Subtract $3$ from both sides of the equation.

$\sqrt[3]{21 x} = - 3$

Step 3

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

${\sqrt[3]{21 x}}^{3} = {(- 3)}^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{21 x}$ as ${(21 x)}^{\frac{1}{3}}$ .

${({(21 x)}^{\frac{1}{3}})}^{3} = {(- 3)}^{3}$

Simplify the left side.

Simplify ${({(21 x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(21 x)}^{\frac{1}{3}})}^{3}$ .

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

${(21 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(21 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Rewrite the expression.

${(21 x)}^{1} = {(- 3)}^{3}$

Simplify.

$21 x = {(- 3)}^{3}$

Simplify the right side.

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

$21 x = - 27$

Step 5

Divide each term in $21 x = - 27$ by $21$ and simplify.

Divide each term in $21 x = - 27$ by $21$ .

$\frac{21 x}{21} = \frac{- 27}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 x}{21} = \frac{- 27}{21}$

Divide $x$ by $1$ .

$x = \frac{- 27}{21}$

Simplify the right side.

Cancel the common factor of $- 27$ and $21$ .

Factor $3$ out of $- 27$ .

$x = \frac{3 (- 9)}{21}$

Cancel the common factors.

Factor $3$ out of $21$ .

$x = \frac{3 \cdot - 9}{3 \cdot 7}$

Cancel the common factor.

$x = \frac{3 \cdot - 9}{3 \cdot 7}$

Rewrite the expression.

$x = \frac{- 9}{7}$

Move the negative in front of the fraction.

$x = - \frac{9}{7}$

Solve by Factoring cube root of 21x=-3

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