Algebra Examples

$\frac{125^{\frac{2}{9}} \cdot 125^{\frac{1}{9}}}{5^{\frac{1}{4}}}$

Step 1

Multiply $125^{\frac{2}{9}}$ by $125^{\frac{1}{9}}$ by adding the exponents.

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Step 1.1

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

$\frac{125^{\frac{2}{9} + \frac{1}{9}}}{5^{\frac{1}{4}}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{125^{\frac{2 + 1}{9}}}{5^{\frac{1}{4}}}$

Step 1.3

Add $2$ and $1$ .

$\frac{125^{\frac{3}{9}}}{5^{\frac{1}{4}}}$

Step 1.4

Cancel the common factor of $3$ and $9$ .

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Step 1.4.1

Factor $3$ out of $3$ .

$\frac{125^{\frac{3 (1)}{9}}}{5^{\frac{1}{4}}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $3$ out of $9$ .

$\frac{125^{\frac{3 \cdot 1}{3 \cdot 3}}}{5^{\frac{1}{4}}}$

Step 1.4.2.2

Cancel the common factor.

$\frac{125^{\frac{3 \cdot 1}{3 \cdot 3}}}{5^{\frac{1}{4}}}$

Step 1.4.2.3

Rewrite the expression.

$\frac{125^{\frac{1}{3}}}{5^{\frac{1}{4}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $125$ as $5^{3}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$\frac{5^{1}}{5^{\frac{1}{4}}}$

Step 2.4

Evaluate the exponent.

$\frac{5}{5^{\frac{1}{4}}}$

Step 3

Move $5^{\frac{1}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$5 \cdot 5^{- \frac{1}{4}}$

Step 4

Multiply $5$ by $5^{- \frac{1}{4}}$ by adding the exponents.

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Step 4.1

Multiply $5$ by $5^{- \frac{1}{4}}$ .

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Step 4.1.1

Raise $5$ to the power of $1$ .

$5^{1} \cdot 5^{- \frac{1}{4}}$

Step 4.1.2

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

$5^{1 - \frac{1}{4}}$

Step 4.2

Write $1$ as a fraction with a common denominator.

$5^{\frac{4}{4} - \frac{1}{4}}$

Step 4.3

Combine the numerators over the common denominator.

$5^{\frac{4 - 1}{4}}$

Step 4.4

Subtract $1$ from $4$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.34370152 \dots$