Solve (a^2b)^4div(a^2b)^2

$$( a ^ { 2 } b ) ^ { 4 } \div ( a ^ { 2 } b ) ^ { 2 }$$

Evaluate

$$b^{2}a^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

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

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

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

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

$$a^{4}b^{2}$$

Expand

$$b^{2}a^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

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

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

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

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

$$a^{4}b^{2}$$