Solve a^-2b^3div(a^2b)^-3=

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

Evaluate

$$a^{4}b^{6}$$

Solution Steps

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

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

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

$$\frac{a^{-2}b^{3}}{a^{-6}b^{-3}}$$

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

$$a^{4}b^{6}$$

Expand

$$a^{4}b^{6}$$

Solution Steps

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

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

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

$$\frac{a^{-2}b^{3}}{a^{-6}b^{-3}}$$

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

$$a^{4}b^{6}$$