Basic Math Examples

{(\frac{4 a b^{- 3}}{3 b})}^{3}

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

Step 1

Move

b^{- 3}

$b^{- 3}$ to the denominator using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

{(\frac{4 a}{3 b \cdot b^{3}})}^{3}

${(\frac{4 a}{3 b \cdot b^{3}})}^{3}$

Step 2

Multiply

b

$b$ by

b^{3}

$b^{3}$ by adding the exponents.

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Step 2.1

Move

b^{3}

$b^{3}$ .

{(\frac{4 a}{3 (b^{3} b)})}^{3}

${(\frac{4 a}{3 (b^{3} b)})}^{3}$

Step 2.2

Multiply

b^{3}

$b^{3}$ by

b

$b$ .

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Step 2.2.1

Raise

b

$b$ to the power of

1

$1$ .

{(\frac{4 a}{3 (b^{3} b^{1})})}^{3}

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

Step 2.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

{(\frac{4 a}{3 b^{3 + 1}})}^{3}

${(\frac{4 a}{3 b^{3 + 1}})}^{3}$

{(\frac{4 a}{3 b^{3 + 1}})}^{3}

${(\frac{4 a}{3 b^{3 + 1}})}^{3}$

Step 2.3

Add

3

$3$ and

1

$1$ .

{(\frac{4 a}{3 b^{4}})}^{3}

${(\frac{4 a}{3 b^{4}})}^{3}$

{(\frac{4 a}{3 b^{4}})}^{3}

${(\frac{4 a}{3 b^{4}})}^{3}$

Step 3

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to

\frac{4 a}{3 b^{4}}

$\frac{4 a}{3 b^{4}}$ .

\frac{{(4 a)}^{3}}{{(3 b^{4})}^{3}}

$\frac{{(4 a)}^{3}}{{(3 b^{4})}^{3}}$

Step 3.2

Apply the product rule to

4 a

$4 a$ .

\frac{4^{3} a^{3}}{{(3 b^{4})}^{3}}

$\frac{4^{3} a^{3}}{{(3 b^{4})}^{3}}$

Step 3.3

Apply the product rule to

3 b^{4}

$3 b^{4}$ .

\frac{4^{3} a^{3}}{3^{3} {(b^{4})}^{3}}

$\frac{4^{3} a^{3}}{3^{3} {(b^{4})}^{3}}$

$\frac{4^{3} a^{3}}{3^{3} {(b^{4})}^{3}}$

Step 4

Raise

$4$ to the power of

$3$ .

$\frac{64 a^{3}}{3^{3} {(b^{4})}^{3}}$

Step 5

Simplify the denominator.

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Step 5.1

Raise

$3$ to the power of

$3$ .

$\frac{64 a^{3}}{27 {(b^{4})}^{3}}$

Step 5.2

Multiply the exponents in

${(b^{4})}^{3}$ .

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Step 5.2.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{64 a^{3}}{27 b^{4 \cdot 3}}$

Step 5.2.2

Multiply

$4$ by

$3$ .

$\frac{64 a^{3}}{27 b^{12}}$

$\frac{64 a^{3}}{27 b^{12}}$

$\frac{64 a^{3}}{27 b^{12}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$