Simplify (-3a^-2b^3)/(15a^-7b^-1)

$\frac{- 3 a^{- 2} b^{3}}{15 a^{- 7} b^{- 1}}$

Step 1

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

$\frac{- 3 a^{- 2} b^{3} a^{7}}{15 b^{- 1}}$

Step 2

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

$\frac{- 3 a^{- 2} b^{3} a^{7} b}{15}$

Step 3

Simplify the numerator.

Multiply $a^{- 2}$ by $a^{7}$ by adding the exponents.

Move $a^{7}$ .

$\frac{- 3 (a^{7} a^{- 2}) b^{3} b}{15}$

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

$\frac{- 3 a^{7 - 2} b^{3} b}{15}$

Subtract $2$ from $7$ .

$\frac{- 3 a^{5} b^{3} b}{15}$

Multiply $b^{3}$ by $b$ by adding the exponents.

Move $b$ .

$\frac{- 3 a^{5} (b \cdot b^{3})}{15}$

Multiply $b$ by $b^{3}$ .

Raise $b$ to the power of $1$ .

$\frac{- 3 a^{5} (b^{1} b^{3})}{15}$

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

$\frac{- 3 a^{5} b^{1 + 3}}{15}$

Add $1$ and $3$ .

$\frac{- 3 a^{5} b^{4}}{15}$

Step 4

Cancel the common factor of $- 3$ and $15$ .

Factor $3$ out of $- 3 a^{5} b^{4}$ .

$\frac{3 (- a^{5} b^{4})}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$\frac{3 (- a^{5} b^{4})}{3 (5)}$

Cancel the common factor.

$\frac{3 (- a^{5} b^{4})}{3 \cdot 5}$

Rewrite the expression.

$\frac{- a^{5} b^{4}}{5}$

Step 5

Move the negative in front of the fraction.

$- \frac{a^{5} b^{4}}{5}$