Solve frac{(a^{2}b^-2)^-2}{(a^-3b)^3}

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

Evaluate

$$ba^{5}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

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

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{a^{-4}b^{4}}{a^{-9}b^{3}}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{a^{-4}b}{a^{-9}}$$

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

$$ba^{5}$$

Expand

$$ba^{5}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

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

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{a^{-4}b^{4}}{a^{-9}b^{3}}$$

Cancel out b^{3} in both numerator and denominator.

$$\frac{a^{-4}b}{a^{-9}}$$

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

$$ba^{5}$$