Solve (a^2b^3)^2/(ab)^-2

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

Evaluate

$$a^{6}b^{8}$$

Solution Steps

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

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

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

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

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

$$\frac{a^{4}b^{6}}{\left(ab\right)^{-2}}$$

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

$$\frac{a^{4}b^{6}}{a^{-2}b^{-2}}$$

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

$$a^{6}b^{8}$$

Expand

$$a^{6}b^{8}$$

Solution Steps

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

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

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

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

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

$$\frac{a^{4}b^{6}}{\left(ab\right)^{-2}}$$

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

$$\frac{a^{4}b^{6}}{a^{-2}b^{-2}}$$

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

$$a^{6}b^{8}$$