Solve (-2a^2b)^3div4a^2b^3

$$( - 2 a ^ { 2 } b ) ^ { 3 } \div 4 a ^ { 2 } b ^ { 3 }$$

Evaluate

$$-2b^{6}a^{8}$$

Solution Steps

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

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

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

$$\frac{\left(-2\right)^{3}a^{6}b^{3}}{4}a^{2}b^{3}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8a^{6}b^{3}}{4}a^{2}b^{3}$$

Divide -8a^{6}b^{3} by 4 to get -2a^{6}b^{3}.

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

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$-2a^{8}b^{3}b^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-2a^{8}b^{6}$$

Expand

$$-2b^{6}a^{8}$$

Solution Steps

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

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

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

$$\frac{\left(-2\right)^{3}a^{6}b^{3}}{4}a^{2}b^{3}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8a^{6}b^{3}}{4}a^{2}b^{3}$$

Divide -8a^{6}b^{3} by 4 to get -2a^{6}b^{3}.

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

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$-2a^{8}b^{3}b^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-2a^{8}b^{6}$$