Pre-Algebra Examples

$\frac{5 a b^{- 3}}{5^{- 1} a^{- 7} b^{3}}$

Step 1

Move $b^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5 a}{5^{- 1} a^{- 7} b^{3} b^{3}}$

Step 2

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

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Step 2.1

Move $b^{3}$ .

$\frac{5 a}{5^{- 1} a^{- 7} (b^{3} b^{3})}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 a}{5^{- 1} a^{- 7} b^{3 + 3}}$

Step 2.3

Add $3$ and $3$ .

$\frac{5 a}{5^{- 1} a^{- 7} b^{6}}$

Step 3

Move $a^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{5 a \cdot a^{7}}{5^{- 1} b^{6}}$

Step 4

Move $5^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{5 a \cdot a^{7} \cdot 5}{b^{6}}$

Step 5

Multiply $a$ by $a^{7}$ by adding the exponents.

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Step 5.1

Move $a^{7}$ .

$\frac{5 (a^{7} a) \cdot 5}{b^{6}}$

Step 5.2

Multiply $a^{7}$ by $a$ .

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Step 5.2.1

Raise $a$ to the power of $1$ .

$\frac{5 (a^{7} a^{1}) \cdot 5}{b^{6}}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 a^{7 + 1} \cdot 5}{b^{6}}$

Step 5.3

Add $7$ and $1$ .

$\frac{5 a^{8} \cdot 5}{b^{6}}$

Step 6

Multiply $5$ by $5$ .

$\frac{25 a^{8}}{b^{6}}$