Basic Math Examples

$\frac{5^{4} \cdot 8^{- 6} \cdot 9^{- 12}}{5^{- 2} \cdot 8^{3} \cdot 9^{- 4}}$

Step 1

Move $8^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5^{4} \cdot 9^{- 12}}{5^{- 2} \cdot 8^{3} \cdot 9^{- 4} \cdot 8^{6}}$

Step 2

Move $9^{- 12}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5^{4}}{5^{- 2} \cdot 8^{3} \cdot 9^{- 4} \cdot 8^{6} \cdot 9^{12}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $8^{3}$ by $8^{6}$ by adding the exponents.

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Step 3.1.1

Move $8^{6}$ .

$\frac{5^{4}}{5^{- 2} \cdot (8^{6} \cdot 8^{3}) \cdot 9^{- 4} \cdot 9^{12}}$

Step 3.1.2

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

$\frac{5^{4}}{5^{- 2} \cdot 8^{6 + 3} \cdot 9^{- 4} \cdot 9^{12}}$

Step 3.1.3

Add $6$ and $3$ .

$\frac{5^{4}}{5^{- 2} \cdot 8^{9} \cdot 9^{- 4} \cdot 9^{12}}$

Step 3.2

Multiply $9^{- 4}$ by $9^{12}$ by adding the exponents.

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Step 3.2.1

Move $9^{12}$ .

$\frac{5^{4}}{5^{- 2} \cdot 8^{9} \cdot (9^{12} \cdot 9^{- 4})}$

Step 3.2.2

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

$\frac{5^{4}}{5^{- 2} \cdot 8^{9} \cdot 9^{12 - 4}}$

Step 3.2.3

Subtract $4$ from $12$ .

$\frac{5^{4}}{5^{- 2} \cdot 8^{9} \cdot 9^{8}}$

Step 4

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

$\frac{5^{4} \cdot 5^{2}}{8^{9} \cdot 9^{8}}$

Step 5

Multiply $5^{4}$ by $5^{2}$ by adding the exponents.

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Step 5.1

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

$\frac{5^{4 + 2}}{8^{9} \cdot 9^{8}}$

Step 5.2

Add $4$ and $2$ .

$\frac{5^{6}}{8^{9} \cdot 9^{8}}$

Step 6

Raise $5$ to the power of $6$ .

$\frac{15625}{8^{9} \cdot 9^{8}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $8$ to the power of $9$ .

$\frac{15625}{134217728 \cdot 9^{8}}$

Step 7.2

Raise $9$ to the power of $8$ .

$\frac{15625}{134217728 \cdot 43046721}$

Step 8

Multiply $134217728$ by $43046721$ .

$\frac{15625}{5777633090469888}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{15625}{5777633090469888}$

Decimal Form:

$2.70439464 \cdot 10^{- 12}$