Algebra Examples

$\frac{25^{\frac{1}{6}} \cdot 25^{\frac{1}{3}}}{5^{\frac{6}{5}}}$

Step 1

Multiply $25^{\frac{1}{6}}$ by $25^{\frac{1}{3}}$ 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.

$\frac{25^{\frac{1}{6} + \frac{1}{3}}}{5^{\frac{6}{5}}}$

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25^{\frac{1}{6} + \frac{1}{3} \cdot \frac{2}{2}}}{5^{\frac{6}{5}}}$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{25^{\frac{1}{6} + \frac{2}{3 \cdot 2}}}{5^{\frac{6}{5}}}$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{25^{\frac{1}{6} + \frac{2}{6}}}{5^{\frac{6}{5}}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{25^{\frac{1 + 2}{6}}}{5^{\frac{6}{5}}}$

Step 1.5

Add $1$ and $2$ .

$\frac{25^{\frac{3}{6}}}{5^{\frac{6}{5}}}$

Step 1.6

Cancel the common factor of $3$ and $6$ .

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Step 1.6.1

Factor $3$ out of $3$ .

$\frac{25^{\frac{3 (1)}{6}}}{5^{\frac{6}{5}}}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $6$ .

$\frac{25^{\frac{3 \cdot 1}{3 \cdot 2}}}{5^{\frac{6}{5}}}$

Step 1.6.2.2

Cancel the common factor.

$\frac{25^{\frac{3 \cdot 1}{3 \cdot 2}}}{5^{\frac{6}{5}}}$

Step 1.6.2.3

Rewrite the expression.

$\frac{25^{\frac{1}{2}}}{5^{\frac{6}{5}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$\frac{{(5^{2})}^{\frac{1}{2}}}{5^{\frac{6}{5}}}$

Step 2.2

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

$\frac{5^{2 (\frac{1}{2})}}{5^{\frac{6}{5}}}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$\frac{5^{2 (\frac{1}{2})}}{5^{\frac{6}{5}}}$

Step 2.3.2

Rewrite the expression.

$\frac{5^{1}}{5^{\frac{6}{5}}}$

Step 2.4

Evaluate the exponent.

$\frac{5}{5^{\frac{6}{5}}}$

Step 3

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

$\frac{1}{5^{\frac{6}{5}} \cdot 5^{- 1}}$

Step 4

Multiply $5^{\frac{6}{5}}$ by $5^{- 1}$ by adding the exponents.

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Step 4.1

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

$\frac{1}{5^{\frac{6}{5} - 1}}$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{5^{\frac{6}{5} - 1 \cdot \frac{5}{5}}}$

Step 4.3

Combine $- 1$ and $\frac{5}{5}$ .

$\frac{1}{5^{\frac{6}{5} + \frac{- 1 \cdot 5}{5}}}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{1}{5^{\frac{6 - 1 \cdot 5}{5}}}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $5$ .

$\frac{1}{5^{\frac{6 - 5}{5}}}$

Step 4.5.2

Subtract $5$ from $6$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.72477966 \dots$