Basic Math Examples

$\frac{4^{- 3} a^{8} b^{6}}{5^{- 2} a^{3} b^{- 9}}$

Step 1

Move $4^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{a^{8} b^{6}}{5^{- 2} a^{3} b^{- 9} \cdot 4^{3}}$

Step 2

Move $b^{- 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{8} b^{6} b^{9}}{5^{- 2} a^{3} \cdot 4^{3}}$

Step 3

Move $5^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{8} b^{6} b^{9} \cdot 5^{2}}{a^{3} \cdot 4^{3}}$

Step 4

Multiply $b^{6}$ by $b^{9}$ by adding the exponents.

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Step 4.1

Move $b^{9}$ .

$\frac{a^{8} (b^{9} b^{6}) \cdot 5^{2}}{a^{3} \cdot 4^{3}}$

Step 4.2

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

$\frac{a^{8} b^{9 + 6} \cdot 5^{2}}{a^{3} \cdot 4^{3}}$

Step 4.3

Add $9$ and $6$ .

$\frac{a^{8} b^{15} \cdot 5^{2}}{a^{3} \cdot 4^{3}}$

Step 5

Cancel the common factor of $a^{8}$ and $a^{3}$ .

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Step 5.1

Factor $a^{3}$ out of $a^{8} b^{15} \cdot 5^{2}$ .

$\frac{a^{3} (a^{5} b^{15} \cdot 5^{2})}{a^{3} \cdot 4^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $a^{3}$ out of $a^{3} \cdot 4^{3}$ .

$\frac{a^{3} (a^{5} b^{15} \cdot 5^{2})}{a^{3} (4^{3})}$

Step 5.2.2

Cancel the common factor.

$\frac{a^{3} (a^{5} b^{15} \cdot 5^{2})}{a^{3} \cdot 4^{3}}$

Step 5.2.3

Rewrite the expression.

$\frac{a^{5} b^{15} \cdot 5^{2}}{4^{3}}$

Step 6

Simplify the expression.

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Step 6.1

Raise $5$ to the power of $2$ .

$\frac{a^{5} b^{15} \cdot 25}{4^{3}}$

Step 6.2

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

$\frac{a^{5} b^{15} \cdot 25}{64}$

Step 6.3

Move $25$ to the left of $a^{5} b^{15}$ .

$\frac{25 a^{5} b^{15}}{64}$