Solve (-12a^{4}b^{3}):(-3ab^2)-(-45a^3b^2):(-9b)+7a(-2a^2b)

$$( - 12 a ^ { 4 } b ^ { 3 } ) : ( - 3 a b ^ { 2 } ) - ( - 45 a ^ { 3 } b ^ { 2 } ) : ( - 9 b ) + 7 a ( - 2 a ^ { 2 } b )$$

Evaluate

$$-15ba^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-12a^{4}b^{3}}{-3ab^{2}}-\frac{-45a^{3}b^{2}}{-9b}+7a^{3}\left(-2\right)b$$

Cancel out 3ab^{2} in both numerator and denominator.

$$\frac{-4ba^{3}}{-1}-\frac{-45a^{3}b^{2}}{-9b}+7a^{3}\left(-2\right)b$$

Anything divided by -1 gives its opposite.

$$4ba^{3}-\frac{-45a^{3}b^{2}}{-9b}+7a^{3}\left(-2\right)b$$

Cancel out 9b in both numerator and denominator.

$$4ba^{3}-\frac{-5ba^{3}}{-1}+7a^{3}\left(-2\right)b$$

Anything divided by -1 gives its opposite.

$$4ba^{3}-5ba^{3}+7a^{3}\left(-2\right)b$$

Multiply 7 and -2 to get -14.

$$4ba^{3}-5ba^{3}-14a^{3}b$$

Combine 4ba^{3} and -14a^{3}b to get -10ba^{3}.

$$-10ba^{3}-5ba^{3}$$

Combine -10ba^{3} and -5ba^{3} to get -15ba^{3}.

$$-15ba^{3}$$

Differentiate w.r.t. b

$$-15a^{3}$$