Pre-Algebra Examples

\frac{2 (a^{3})}{\frac{b}{\frac{5}{b^{2}}}}

$\frac{2 (a^{3})}{\frac{b}{\frac{5}{b^{2}}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

2 a^{3} \frac{\frac{5}{b^{2}}}{b}

$2 a^{3} \frac{\frac{5}{b^{2}}}{b}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

2 a^{3} (\frac{5}{b^{2}} \cdot \frac{1}{b})

$2 a^{3} (\frac{5}{b^{2}} \cdot \frac{1}{b})$

Step 3

Combine.

2 a^{3} \frac{5 \cdot 1}{b^{2} b}

$2 a^{3} \frac{5 \cdot 1}{b^{2} b}$

Step 4

Multiply

b^{2}

$b^{2}$ by

b

$b$ by adding the exponents.

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Step 4.1

Multiply

b^{2}

$b^{2}$ by

b

$b$ .

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Step 4.1.1

Raise

b

$b$ to the power of

1

$1$ .

2 a^{3} \frac{5 \cdot 1}{b^{2} b^{1}}

$2 a^{3} \frac{5 \cdot 1}{b^{2} b^{1}}$

Step 4.1.2

Use the power rule

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

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

2 a^{3} \frac{5 \cdot 1}{b^{2 + 1}}

$2 a^{3} \frac{5 \cdot 1}{b^{2 + 1}}$

2 a^{3} \frac{5 \cdot 1}{b^{2 + 1}}

$2 a^{3} \frac{5 \cdot 1}{b^{2 + 1}}$

Step 4.2

Add

2

$2$ and

1

$1$ .

2 a^{3} \frac{5 \cdot 1}{b^{3}}

$2 a^{3} \frac{5 \cdot 1}{b^{3}}$

2 a^{3} \frac{5 \cdot 1}{b^{3}}

$2 a^{3} \frac{5 \cdot 1}{b^{3}}$

Step 5

Multiply

5

$5$ by

1

$1$ .

2 a^{3} \frac{5}{b^{3}}

$2 a^{3} \frac{5}{b^{3}}$

Step 6

Multiply

2 a^{3} \frac{5}{b^{3}}

$2 a^{3} \frac{5}{b^{3}}$ .

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Step 6.1

Combine

2

$2$ and

\frac{5}{b^{3}}

$\frac{5}{b^{3}}$ .

a^{3} \frac{2 \cdot 5}{b^{3}}

$a^{3} \frac{2 \cdot 5}{b^{3}}$

Step 6.2

Multiply

2

$2$ by

5

$5$ .

a^{3} \frac{10}{b^{3}}

$a^{3} \frac{10}{b^{3}}$

Step 6.3

Combine

a^{3}

$a^{3}$ and

\frac{10}{b^{3}}

$\frac{10}{b^{3}}$ .

\frac{a^{3} \cdot 10}{b^{3}}

$\frac{a^{3} \cdot 10}{b^{3}}$

\frac{a^{3} \cdot 10}{b^{3}}

$\frac{a^{3} \cdot 10}{b^{3}}$

Step 7

Move

10

$10$ to the left of

a^{3}

$a^{3}$ .

\frac{10 a^{3}}{b^{3}}

$\frac{10 a^{3}}{b^{3}}$