Solve (4c^{3}b^2)^-1(-3c^2b^3)

$$( 4 c ^ { 3 } b ^ { 2 } ) ^ { - 1 } ( - 3 c ^ { 2 } b ^ { 3 } )$$

Evaluate

$$-\frac{3b}{4c}$$

Solution Steps

Expand \left(4c^{3}b^{2}\right)^{-1}.

$$4^{-1}\left(c^{3}\right)^{-1}\left(b^{2}\right)^{-1}\left(-3\right)c^{2}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$4^{-1}c^{-3}\left(b^{2}\right)^{-1}\left(-3\right)c^{2}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$4^{-1}c^{-3}b^{-2}\left(-3\right)c^{2}b^{3}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$\frac{1}{4}c^{-3}b^{-2}\left(-3\right)c^{2}b^{3}$$

Multiply \frac{1}{4} and -3 to get -\frac{3}{4}.

$$-\frac{3}{4}c^{-3}b^{-2}c^{2}b^{3}$$

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

$$-\frac{3}{4}c^{-1}b^{-2}b^{3}$$

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

$$-\frac{3}{4}c^{-1}b^{1}$$

Calculate b to the power of 1 and get b.

$$-\frac{3}{4}c^{-1}b$$

Differentiate w.r.t. c

$$\frac{3b}{4c^{2}}$$