Calculus Examples

$\frac{625^{\frac{1}{3}} \cdot 5^{\frac{1}{3}}}{25^{\frac{4}{3}}}$

Step 1

Rewrite $625$ as $5^{4}$ .

$\frac{{(5^{4})}^{\frac{1}{3}} \cdot 5^{\frac{1}{3}}}{25^{\frac{4}{3}}}$

Step 2

Multiply the exponents in ${(5^{4})}^{\frac{1}{3}}$ .

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Step 2.1

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

$\frac{5^{4 (\frac{1}{3})} \cdot 5^{\frac{1}{3}}}{25^{\frac{4}{3}}}$

Step 2.2

Combine $4$ and $\frac{1}{3}$ .

$\frac{5^{\frac{4}{3}} \cdot 5^{\frac{1}{3}}}{25^{\frac{4}{3}}}$

Step 3

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

$\frac{5^{\frac{4}{3} + \frac{1}{3}}}{25^{\frac{4}{3}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5^{\frac{4 + 1}{3}}}{25^{\frac{4}{3}}}$

Step 5

Add $4$ and $1$ .

$\frac{5^{\frac{5}{3}}}{25^{\frac{4}{3}}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5^{\frac{5}{3}}}{25^{\frac{4}{3}}}$

Decimal Form:

$0.2$