Basic Math Examples

${(\frac{5}{6})}^{3} \div {(\frac{5}{12})}^{4}$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{5}{6})}^{3}}{{(\frac{5}{12})}^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{5}{6}$ .

$\frac{\frac{5^{3}}{6^{3}}}{{(\frac{5}{12})}^{4}}$

Step 2.2

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

$\frac{\frac{125}{6^{3}}}{{(\frac{5}{12})}^{4}}$

Step 2.3

Raise $6$ to the power of $3$ .

$\frac{\frac{125}{216}}{{(\frac{5}{12})}^{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $\frac{5}{12}$ .

$\frac{\frac{125}{216}}{\frac{5^{4}}{12^{4}}}$

Step 3.2

Raise $5$ to the power of $4$ .

$\frac{\frac{125}{216}}{\frac{625}{12^{4}}}$

Step 3.3

Raise $12$ to the power of $4$ .

$\frac{\frac{125}{216}}{\frac{625}{20736}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{125}{216} \cdot \frac{20736}{625}$

Step 5

Cancel the common factor of $125$ .

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Step 5.1

Factor $125$ out of $625$ .

$\frac{125}{216} \cdot \frac{20736}{125 (5)}$

Step 5.2

Cancel the common factor.

$\frac{125}{216} \cdot \frac{20736}{125 \cdot 5}$

Step 5.3

Rewrite the expression.

$\frac{1}{216} \cdot \frac{20736}{5}$

Step 6

Cancel the common factor of $216$ .

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Step 6.1

Factor $216$ out of $20736$ .

$\frac{1}{216} \cdot \frac{216 (96)}{5}$

Step 6.2

Cancel the common factor.

$\frac{1}{216} \cdot \frac{216 \cdot 96}{5}$

Step 6.3

Rewrite the expression.

$\frac{96}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{96}{5}$

Decimal Form:

$19.2$

Mixed Number Form:

$19 \frac{1}{5}$