Solve by Factoring cube root of 5x+3- cube root of 4x=0

$\sqrt[3]{5 x + 3} - \sqrt[3]{4 x} = 0$

Step 1

Add $\sqrt[3]{4 x}$ to both sides of the equation.

$\sqrt[3]{5 x + 3} = \sqrt[3]{4 x}$

Step 2

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

${\sqrt[3]{5 x + 3}}^{3} = {\sqrt[3]{4 x}}^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 x + 3}$ as ${(5 x + 3)}^{\frac{1}{3}}$ .

${({(5 x + 3)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{4 x}}^{3}$

Simplify the left side.

Simplify ${({(5 x + 3)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 x + 3)}^{\frac{1}{3}})}^{3}$ .

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

${(5 x + 3)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{4 x}}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 x + 3)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{4 x}}^{3}$

Rewrite the expression.

${(5 x + 3)}^{1} = {\sqrt[3]{4 x}}^{3}$

Simplify.

$5 x + 3 = {\sqrt[3]{4 x}}^{3}$

Simplify the right side.

Rewrite ${\sqrt[3]{4 x}}^{3}$ as $4 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x}$ as ${(4 x)}^{\frac{1}{3}}$ .

$5 x + 3 = {({(4 x)}^{\frac{1}{3}})}^{3}$

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

$5 x + 3 = {(4 x)}^{\frac{1}{3} \cdot 3}$

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

$5 x + 3 = {(4 x)}^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$5 x + 3 = {(4 x)}^{\frac{3}{3}}$

Rewrite the expression.

$5 x + 3 = {(4 x)}^{1}$

Simplify.

$5 x + 3 = 4 x$

Step 4

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$5 x + 3 - 4 x = 0$

Subtract $4 x$ from $5 x$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Solve by Factoring cube root of 5x+3- cube root of 4x=0

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