Solve frac{2ab^{-3}*2ba^2}{(a^2b^2)^0}

$$\frac { 2 a b ^ { - 3 } \cdot 2 b a ^ { 2 } } { ( a ^ { 2 } b ^ { 2 } ) ^ { 0 } }$$

Evaluate

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

Solution Steps

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

$$\frac{2a^{3}b^{-3}\times 2b}{\left(a^{2}b^{2}\right)^{0}}$$

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

$$\frac{2a^{3}b^{-2}\times 2}{\left(a^{2}b^{2}\right)^{0}}$$

Multiply 2 and 2 to get 4.

$$\frac{4a^{3}b^{-2}}{\left(a^{2}b^{2}\right)^{0}}$$

Calculate a^{2}b^{2} to the power of 0 and get 1.

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

Anything divided by one gives itself.

$$4a^{3}b^{-2}$$

Differentiate w.r.t. b

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