Basic Math Examples

$\frac{(\frac{2^{3}}{5^{3}}) \cdot (\frac{5^{- 2}}{2^{- 2}})}{(\frac{4^{2}}{25^{2}}) \cdot (\frac{125^{- 2}}{8^{- 2}})}$

Step 1

Evaluate the exponents.

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Step 1.1

Raise $2$ to the power of $3$ .

$\frac{\frac{8}{5^{3}} \cdot \frac{5^{- 2}}{2^{- 2}}}{\frac{4^{2}}{25^{2}} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 1.2

Raise $5$ to the power of $3$ .

$\frac{\frac{8}{125} \cdot \frac{5^{- 2}}{2^{- 2}}}{\frac{4^{2}}{25^{2}} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{5^{2}}}{2^{- 2}}}{\frac{4^{2}}{25^{2}} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 2.2

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

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{2^{- 2}}}{\frac{4^{2}}{25^{2}} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{2^{2}}}}{\frac{4^{2}}{25^{2}} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 3.2

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

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{4}}}{\frac{4^{2}}{25^{2}} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 4

Evaluate the exponents.

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Step 4.1

Raise $4$ to the power of $2$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{4}}}{\frac{16}{25^{2}} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 4.2

Raise $25$ to the power of $2$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{4}}}{\frac{16}{625} \cdot \frac{125^{- 2}}{8^{- 2}}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{4}}}{\frac{16}{625} \cdot \frac{\frac{1}{125^{2}}}{8^{- 2}}}$

Step 5.2

Raise $125$ to the power of $2$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{4}}}{\frac{16}{625} \cdot \frac{\frac{1}{15625}}{8^{- 2}}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{4}}}{\frac{16}{625} \cdot \frac{\frac{1}{15625}}{\frac{1}{8^{2}}}}$

Step 6.2

Raise $8$ to the power of $2$ .

$\frac{\frac{8}{125} \cdot \frac{\frac{1}{25}}{\frac{1}{4}}}{\frac{16}{625} \cdot \frac{\frac{1}{15625}}{\frac{1}{64}}}$

Step 7

Multiply $\frac{8}{125}$ by $\frac{\frac{1}{25}}{\frac{1}{4}}$ .

$\frac{\frac{8 (\frac{1}{25})}{125 (\frac{1}{4})}}{\frac{16}{625} \cdot \frac{\frac{1}{15625}}{\frac{1}{64}}}$

Step 8

Multiply $\frac{16}{625}$ by $\frac{\frac{1}{15625}}{\frac{1}{64}}$ .

$\frac{\frac{8 (\frac{1}{25})}{125 (\frac{1}{4})}}{\frac{16 (\frac{1}{15625})}{625 (\frac{1}{64})}}$

Step 9

Combine fractions.

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Step 9.1

Combine $8$ and $\frac{1}{25}$ .

$\frac{\frac{\frac{8}{25}}{125 (\frac{1}{4})}}{\frac{16 (\frac{1}{15625})}{625 (\frac{1}{64})}}$

Step 9.2

Combine $125$ and $\frac{1}{4}$ .

$\frac{\frac{\frac{8}{25}}{\frac{125}{4}}}{\frac{16 (\frac{1}{15625})}{625 (\frac{1}{64})}}$

Step 9.3

Combine $16$ and $\frac{1}{15625}$ .

$\frac{\frac{\frac{8}{25}}{\frac{125}{4}}}{\frac{\frac{16}{15625}}{625 (\frac{1}{64})}}$

Step 9.4

Combine $625$ and $\frac{1}{64}$ .

$\frac{\frac{\frac{8}{25}}{\frac{125}{4}}}{\frac{\frac{16}{15625}}{\frac{625}{64}}}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{8}{25} \cdot \frac{4}{125}}{\frac{\frac{16}{15625}}{\frac{625}{64}}}$

Step 10.2

Multiply $\frac{8}{25} \cdot \frac{4}{125}$ .

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Step 10.2.1

Multiply $\frac{8}{25}$ by $\frac{4}{125}$ .

$\frac{\frac{8 \cdot 4}{25 \cdot 125}}{\frac{\frac{16}{15625}}{\frac{625}{64}}}$

Step 10.2.2

Multiply $8$ by $4$ .

$\frac{\frac{32}{25 \cdot 125}}{\frac{\frac{16}{15625}}{\frac{625}{64}}}$

Step 10.2.3

Multiply $25$ by $125$ .

$\frac{\frac{32}{3125}}{\frac{\frac{16}{15625}}{\frac{625}{64}}}$

Step 11

Simplify the denominator.

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Step 11.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{32}{3125}}{\frac{16}{15625} \cdot \frac{64}{625}}$

Step 11.2

Multiply $\frac{16}{15625} \cdot \frac{64}{625}$ .

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Step 11.2.1

Multiply $\frac{16}{15625}$ by $\frac{64}{625}$ .

$\frac{\frac{32}{3125}}{\frac{16 \cdot 64}{15625 \cdot 625}}$

Step 11.2.2

Multiply $16$ by $64$ .

$\frac{\frac{32}{3125}}{\frac{1024}{15625 \cdot 625}}$

Step 11.2.3

Multiply $15625$ by $625$ .

$\frac{\frac{32}{3125}}{\frac{1024}{9765625}}$

Step 12

Multiply the numerator by the reciprocal of the denominator.

$\frac{32}{3125} \cdot \frac{9765625}{1024}$

Step 13

Cancel the common factor of $32$ .

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Step 13.1

Factor $32$ out of $1024$ .

$\frac{32}{3125} \cdot \frac{9765625}{32 (32)}$

Step 13.2

Cancel the common factor.

$\frac{32}{3125} \cdot \frac{9765625}{32 \cdot 32}$

Step 13.3

Rewrite the expression.

$\frac{1}{3125} \cdot \frac{9765625}{32}$

Step 14

Cancel the common factor of $3125$ .

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Step 14.1

Factor $3125$ out of $9765625$ .

$\frac{1}{3125} \cdot \frac{3125 (3125)}{32}$

Step 14.2

Cancel the common factor.

$\frac{1}{3125} \cdot \frac{3125 \cdot 3125}{32}$

Step 14.3

Rewrite the expression.

$\frac{3125}{32}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{3125}{32}$

Decimal Form:

$97.65625$

Mixed Number Form:

$97 \frac{21}{32}$