Solve a^2b/(ab^2)^-2

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

Evaluate

$$a^{4}b^{5}$$

Solution Steps

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

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

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

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

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

$$a^{4}b^{5}$$

Expand

$$a^{4}b^{5}$$

Solution Steps

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

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

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

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

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

$$a^{4}b^{5}$$