Simplify (-4(r^4t^-2)^-1)/(4r^2t^4)

$\frac{- 4 {(r^{4} t^{- 2})}^{- 1}}{4 r^{2} t^{4}}$

Step 1

Move ${(r^{4} t^{- 2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 4}{4 r^{2} t^{4} (r^{4} t^{- 2})}$

Step 2

Simplify the denominator.

Multiply $r^{2}$ by $r^{4}$ by adding the exponents.

Move $r^{4}$ .

$\frac{- 4}{4 (r^{4} r^{2}) t^{4} t^{- 2}}$

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

$\frac{- 4}{4 r^{4 + 2} t^{4} t^{- 2}}$

Add $4$ and $2$ .

$\frac{- 4}{4 r^{6} t^{4} t^{- 2}}$

Multiply $t^{4}$ by $t^{- 2}$ by adding the exponents.

Move $t^{- 2}$ .

$\frac{- 4}{4 r^{6} (t^{- 2} t^{4})}$

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

$\frac{- 4}{4 r^{6} t^{- 2 + 4}}$

Add $- 2$ and $4$ .

$\frac{- 4}{4 r^{6} t^{2}}$

Step 3

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

Factor $4$ out of $- 4$ .

$\frac{4 \cdot - 1}{4 r^{6} t^{2}}$

Cancel the common factors.

Factor $4$ out of $4 r^{6} t^{2}$ .

$\frac{4 \cdot - 1}{4 (r^{6} t^{2})}$

Cancel the common factor.

$\frac{4 \cdot - 1}{4 (r^{6} t^{2})}$

Rewrite the expression.

$\frac{- 1}{r^{6} t^{2}}$

Step 4

Move the negative in front of the fraction.

$- \frac{1}{r^{6} t^{2}}$