Solve (frac{32a^{2}b^{-4}}{4a^-8b^-2})*-8a^-2/-3b^-3

$$( \frac { 32 a ^ { 2 } b ^ { - 4 } } { 4 a ^ { - 8 } b ^ { - 2 } } ) \times \frac { - 8 a ^ { - 2 } } { - 3 b ^ { - 3 } }$$

Evaluate

$$\frac{64ba^{8}}{3}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{8b^{-4}a^{2}}{a^{-8}b^{-2}}\times \frac{-8a^{-2}}{-3b^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{8b^{-4}a^{10}}{b^{-2}}\times \frac{-8a^{-2}}{-3b^{-3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{8a^{10}}{b^{2}}\times \frac{-8a^{-2}}{-3b^{-3}}$$

Multiply \frac{8a^{10}}{b^{2}} times \frac{-8a^{-2}}{-3b^{-3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8a^{10}\left(-8\right)a^{-2}}{b^{2}\left(-3\right)b^{-3}}$$

To multiply powers of the same base, add their exponents. Add 10 and -2 to get 8.

$$\frac{8a^{8}\left(-8\right)}{b^{2}\left(-3\right)b^{-3}}$$

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

$$\frac{8a^{8}\left(-8\right)}{b^{-1}\left(-3\right)}$$

Multiply 8 and -8 to get -64.

$$\frac{-64a^{8}}{b^{-1}\left(-3\right)}$$

Differentiate w.r.t. a

$$\frac{512ba^{7}}{3}$$