Simplify 125^(-3/4)*5^(-3/4)

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Combine fractions.

Combine.

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

Multiply $1$ by $1$ .

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

Step 4

Simplify the denominator.

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

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

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

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

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

Multiply $3 (\frac{3}{4})$ .

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

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

Multiply $3$ by $3$ .

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

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

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

Combine the numerators over the common denominator.

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

Add $9$ and $3$ .

$\frac{1}{5^{\frac{12}{4}}}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3$ by $1$ .

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

Step 5

Raise $5$ to the power of $3$ .

$\frac{1}{125}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{125}$

Decimal Form:

$0.008$

Simplify 125^(-3/4)*5^(-3/4)

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