Algebra Examples

$4 \sqrt[3]{x - 7 + 1} = 9$

Step 1

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

${(4 \sqrt[3]{x - 7 + 1})}^{3} = 9^{3}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

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

${(4 {(x - 7 + 1)}^{\frac{1}{3}})}^{3} = 9^{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${(4 {(x - 7 + 1)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 2.2.1.1

Add $- 7$ and $1$ .

${(4 {(x - 6)}^{\frac{1}{3}})}^{3} = 9^{3}$

Step 2.2.1.2

Apply the product rule to $4 {(x - 6)}^{\frac{1}{3}}$ .

$4^{3} {({(x - 6)}^{\frac{1}{3}})}^{3} = 9^{3}$

Step 2.2.1.3

Raise $4$ to the power of $3$ .

$64 {({(x - 6)}^{\frac{1}{3}})}^{3} = 9^{3}$

Step 2.2.1.4

Multiply the exponents in ${({(x - 6)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 2.2.1.4.1

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

$64 {(x - 6)}^{\frac{1}{3} \cdot 3} = 9^{3}$

Step 2.2.1.4.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.4.2.1

Cancel the common factor.

$64 {(x - 6)}^{\frac{1}{3} \cdot 3} = 9^{3}$

Step 2.2.1.4.2.2

Rewrite the expression.

$64 {(x - 6)}^{1} = 9^{3}$

Step 2.2.1.5

Simplify.

$64 (x - 6) = 9^{3}$

Step 2.2.1.6

Apply the distributive property.

$64 x + 64 \cdot - 6 = 9^{3}$

Step 2.2.1.7

Multiply $64$ by $- 6$ .

$64 x - 384 = 9^{3}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Raise $9$ to the power of $3$ .

$64 x - 384 = 729$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Add $384$ to both sides of the equation.

$64 x = 729 + 384$

Step 3.1.2

Add $729$ and $384$ .

$64 x = 1113$

Step 3.2

Divide each term in $64 x = 1113$ by $64$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $64 x = 1113$ by $64$ .

$\frac{64 x}{64} = \frac{1113}{64}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $64$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{64 x}{64} = \frac{1113}{64}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1113}{64}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1113}{64}$

Decimal Form:

$x = 17.390625$

Mixed Number Form:

$x = 17 \frac{25}{64}$