Solve a^{-2}b^{-3}*(-3a^-1b^2)div6a^-4b^-2

$$a ^ { - 2 } b ^ { - 3 } \cdot ( - 3 a ^ { - 1 } b ^ { 2 } ) \div 6 a ^ { - 4 } b ^ { - 2 }$$

Evaluate

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

Solution Steps

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

$$\frac{a^{-3}b^{-3}\left(-3\right)b^{2}}{6}a^{-4}b^{-2}$$

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

$$\frac{a^{-3}b^{-1}\left(-3\right)}{6}a^{-4}b^{-2}$$

Divide a^{-3}b^{-1}\left(-3\right) by 6 to get a^{-3}b^{-1}\left(-\frac{1}{2}\right).

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

To multiply powers of the same base, add their exponents. Add -3 and -4 to get -7.

$$a^{-7}b^{-1}\left(-\frac{1}{2}\right)b^{-2}$$

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

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

Differentiate w.r.t. a

$$\frac{7}{2b^{3}a^{8}}$$