Solve frac{(a^{2}b^-2)^-3}{ab}*a^7b^-5

$$\frac { ( a ^ { 2 } b ^ { - 2 } ) ^ { - 3 } } { a b } \cdot a ^ { 7 } b ^ { - 5 }$$

Evaluate

$$1$$

Solution Steps

Expand \left(a^{2}b^{-2}\right)^{-3}.

$$\frac{\left(a^{2}\right)^{-3}\left(b^{-2}\right)^{-3}}{ab}a^{7}b^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{a^{-6}\left(b^{-2}\right)^{-3}}{ab}a^{7}b^{-5}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{a^{-6}b^{6}}{ab}a^{7}b^{-5}$$

Cancel out b in both numerator and denominator.

$$\frac{a^{-6}b^{5}}{a}a^{7}b^{-5}$$

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

$$\frac{b^{5}}{a^{7}}a^{7}b^{-5}$$

Cancel out a^{7} and a^{7}.

$$b^{5}b^{-5}$$

Multiply b^{5} and b^{-5} to get 1.

$$1$$

Factor

$$1$$