Algebra Examples

${(m^{\frac{3}{4}} n)}^{- 2}$

Step 1

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

$\frac{1}{{(m^{\frac{3}{4}} n)}^{2}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $m^{\frac{3}{4}} n$ .

$\frac{1}{{(m^{\frac{3}{4}})}^{2} n^{2}}$

Step 2.2

Multiply the exponents in ${(m^{\frac{3}{4}})}^{2}$ .

Tap for more steps...

Step 2.2.1

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

$\frac{1}{m^{\frac{3}{4} \cdot 2} n^{2}}$

Step 2.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.2.1

Factor $2$ out of $4$ .

$\frac{1}{m^{\frac{3}{2 (2)} \cdot 2} n^{2}}$

Step 2.2.2.2

Cancel the common factor.

$\frac{1}{m^{\frac{3}{2 \cdot 2} \cdot 2} n^{2}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{1}{m^{\frac{3}{2}} n^{2}}$

Step 3

Reorder factors in $\frac{1}{m^{\frac{3}{2}} n^{2}}$ .

$\frac{1}{n^{2} m^{\frac{3}{2}}}$