Evaluate (25^(1/6))/(25^(2/3))

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

Step 1

Move $25^{\frac{1}{6}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

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

Step 2

Multiply $25^{\frac{2}{3}}$ by $25^{- \frac{1}{6}}$ by adding the exponents.

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

$\frac{1}{25^{\frac{2}{3} - \frac{1}{6}}}$

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

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

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

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

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

Multiply $3$ by $2$ .

$\frac{1}{25^{\frac{2 \cdot 2}{6} - \frac{1}{6}}}$

Combine the numerators over the common denominator.

$\frac{1}{25^{\frac{2 \cdot 2 - 1}{6}}}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{1}{25^{\frac{4 - 1}{6}}}$

Subtract $1$ from $4$ .

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

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

Factor $3$ out of $3$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$

Evaluate (25^(1/6))/(25^(2/3))

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