Basic Math Examples

${(3^{\frac{4}{5}})}^{5} \cdot 5^{\frac{2}{3}} \div 5^{2}$

Step 1

Rewrite the division as a fraction.

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

Step 2

Move $5^{\frac{2}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

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

Step 3

Multiply $5^{2}$ by $5^{- \frac{2}{3}}$ by adding the exponents.

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Step 3.1

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

$\frac{{(3^{\frac{4}{5}})}^{5}}{5^{2 - \frac{2}{3}}}$

Step 3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

Combine $2$ and $\frac{3}{3}$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $3$ .

$\frac{{(3^{\frac{4}{5}})}^{5}}{5^{\frac{6 - 2}{3}}}$

Step 3.5.2

Subtract $2$ from $6$ .

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply the exponents in ${(3^{\frac{4}{5}})}^{5}$ .

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Step 4.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{\frac{4}{5} \cdot 5}}{5^{\frac{4}{3}}}$

Step 4.1.2

Cancel the common factor of $5$ .

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Step 4.1.2.1

Cancel the common factor.

$\frac{3^{\frac{4}{5} \cdot 5}}{5^{\frac{4}{3}}}$

Step 4.1.2.2

Rewrite the expression.

$\frac{3^{4}}{5^{\frac{4}{3}}}$

Step 4.2

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

$\frac{81}{5^{\frac{4}{3}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{5^{\frac{4}{3}}}$

Decimal Form:

$9.47381747 \dots$