Simplify ((4s^5t^-7)/(-2s^-2t^4))

$(\frac{4 s^{5} t^{- 7}}{- 2 s^{- 2} t^{4}})$

Step 1

Remove parentheses.

$\frac{4 s^{5} t^{- 7}}{- 2 s^{- 2} t^{4}}$

Step 2

Move $t^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 s^{5}}{- 2 s^{- 2} t^{4} t^{7}}$

Step 3

Multiply $t^{4}$ by $t^{7}$ by adding the exponents.

Move $t^{7}$ .

$\frac{4 s^{5}}{- 2 s^{- 2} (t^{7} t^{4})}$

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

$\frac{4 s^{5}}{- 2 s^{- 2} t^{7 + 4}}$

Add $7$ and $4$ .

$\frac{4 s^{5}}{- 2 s^{- 2} t^{11}}$

Step 4

Move $s^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4 s^{5} s^{2}}{- 2 t^{11}}$

Step 5

Multiply $s^{5}$ by $s^{2}$ by adding the exponents.

Move $s^{2}$ .

$\frac{4 (s^{2} s^{5})}{- 2 t^{11}}$

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

$\frac{4 s^{2 + 5}}{- 2 t^{11}}$

Add $2$ and $5$ .

$\frac{4 s^{7}}{- 2 t^{11}}$

Step 6

Cancel the common factor of $4$ and $- 2$ .

Factor $2$ out of $4 s^{7}$ .

$\frac{2 (2 s^{7})}{- 2 t^{11}}$

Cancel the common factors.

Factor $2$ out of $- 2 t^{11}$ .

$\frac{2 (2 s^{7})}{2 (- t^{11})}$

Cancel the common factor.

$\frac{2 (2 s^{7})}{2 (- t^{11})}$

Rewrite the expression.

$\frac{2 s^{7}}{- t^{11}}$

Step 7

Move the negative in front of the fraction.

$- \frac{2 s^{7}}{t^{11}}$