Basic Math Examples

$4 \cdot \sqrt[3]{a - 1} - 4 = 0$

Step 1

Add $4$ to both sides of the equation.

$4 \cdot \sqrt[3]{a - 1} = 4$

Step 2

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

${(4 \cdot \sqrt[3]{a - 1})}^{3} = 4^{3}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

${(4 \cdot {(a - 1)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(4 \cdot {(a - 1)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1

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

$4^{3} {({(a - 1)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 3.2.1.2

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

$64 {({(a - 1)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 3.2.1.3

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

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Step 3.2.1.3.1

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

$64 {(a - 1)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 3.2.1.3.2

Cancel the common factor of $3$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$64 {(a - 1)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 3.2.1.3.2.2

Rewrite the expression.

$64 {(a - 1)}^{1} = 4^{3}$

Step 3.2.1.4

Simplify.

$64 (a - 1) = 4^{3}$

Step 3.2.1.5

Apply the distributive property.

$64 a + 64 \cdot - 1 = 4^{3}$

Step 3.2.1.6

Multiply $64$ by $- 1$ .

$64 a - 64 = 4^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$64 a - 64 = 64$

Step 4

Solve for $a$ .

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Step 4.1

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

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Step 4.1.1

Add $64$ to both sides of the equation.

$64 a = 64 + 64$

Step 4.1.2

Add $64$ and $64$ .

$64 a = 128$

Step 4.2

Divide each term in $64 a = 128$ by $64$ and simplify.

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Step 4.2.1

Divide each term in $64 a = 128$ by $64$ .

$\frac{64 a}{64} = \frac{128}{64}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $64$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{64 a}{64} = \frac{128}{64}$

Step 4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{128}{64}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $128$ by $64$ .

$a = 2$