Solve (2)(-2a^{2}b)^2*(-1/2a^2b^2)^3

$$( 2 ) ( - 2 a ^ { 2 } b ) ^ { 2 } \cdot ( - \frac { 1 } { 2 } a ^ { 2 } b ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-b^{8}a^{10}$$

Solution Steps

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

$$2\left(-2\right)^{2}\left(a^{2}\right)^{2}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

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

$$2\left(-2\right)^{2}a^{4}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

Calculate -2 to the power of 2 and get 4.

$$2\times 4a^{4}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

Multiply 2 and 4 to get 8.

$$8a^{4}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

Expand \left(-\frac{1}{2}a^{2}b^{2}\right)^{3}.

$$8a^{4}b^{2}\left(-\frac{1}{2}\right)^{3}\left(a^{2}\right)^{3}\left(b^{2}\right)^{3}$$

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

$$8a^{4}b^{2}\left(-\frac{1}{2}\right)^{3}a^{6}\left(b^{2}\right)^{3}$$

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

$$8a^{4}b^{2}\left(-\frac{1}{2}\right)^{3}a^{6}b^{6}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$8a^{4}b^{2}\left(-\frac{1}{8}\right)a^{6}b^{6}$$

Multiply 8 and -\frac{1}{8} to get -1.

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

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$-a^{10}b^{2}b^{6}$$

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

$$-a^{10}b^{8}$$

Expand

$$-b^{8}a^{10}$$

Solution Steps

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

$$2\left(-2\right)^{2}\left(a^{2}\right)^{2}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

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

$$2\left(-2\right)^{2}a^{4}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

Calculate -2 to the power of 2 and get 4.

$$2\times 4a^{4}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

Multiply 2 and 4 to get 8.

$$8a^{4}b^{2}\left(-\frac{1}{2}a^{2}b^{2}\right)^{3}$$

Expand \left(-\frac{1}{2}a^{2}b^{2}\right)^{3}.

$$8a^{4}b^{2}\left(-\frac{1}{2}\right)^{3}\left(a^{2}\right)^{3}\left(b^{2}\right)^{3}$$

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

$$8a^{4}b^{2}\left(-\frac{1}{2}\right)^{3}a^{6}\left(b^{2}\right)^{3}$$

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

$$8a^{4}b^{2}\left(-\frac{1}{2}\right)^{3}a^{6}b^{6}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$8a^{4}b^{2}\left(-\frac{1}{8}\right)a^{6}b^{6}$$

Multiply 8 and -\frac{1}{8} to get -1.

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

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$-a^{10}b^{2}b^{6}$$

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

$$-a^{10}b^{8}$$