Simplify (-3(v^3)^-5)/(6s^-7)

$\frac{- 3 {(v^{3})}^{- 5}}{6 s^{- 7}}$

Step 1

Simplify.

Move ${(v^{3})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 3}{6 s^{- 7} {(v^{3})}^{5}}$

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

$\frac{- 3 s^{7}}{6 {(v^{3})}^{5}}$

Step 2

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

Factor $3$ out of $- 3 s^{7}$ .

$\frac{3 (- s^{7})}{6 {(v^{3})}^{5}}$

Cancel the common factors.

Factor $3$ out of $6 {(v^{3})}^{5}$ .

$\frac{3 (- s^{7})}{3 (2 {(v^{3})}^{5})}$

Cancel the common factor.

$\frac{3 (- s^{7})}{3 (2 {(v^{3})}^{5})}$

Rewrite the expression.

$\frac{- s^{7}}{2 {(v^{3})}^{5}}$

Step 3

Simplify the expression.

Multiply the exponents in ${(v^{3})}^{5}$ .

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

$\frac{- s^{7}}{2 v^{3 \cdot 5}}$

Multiply $3$ by $5$ .

$\frac{- s^{7}}{2 v^{15}}$

Move the negative in front of the fraction.

$- \frac{s^{7}}{2 v^{15}}$