Solve (8x^2y)(-1/2xy^2)^3

$$( 8 x ^ { 2 } y ) ( - \frac { 1 } { 2 } x y ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-x^{5}y^{7}$$

Solution Steps

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

$$8x^{2}y\left(-\frac{1}{2}\right)^{3}x^{3}\left(y^{2}\right)^{3}$$

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

$$8x^{2}y\left(-\frac{1}{2}\right)^{3}x^{3}y^{6}$$

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

$$8x^{2}y\left(-\frac{1}{8}\right)x^{3}y^{6}$$

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

$$-x^{2}yx^{3}y^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-x^{5}yy^{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$-x^{5}y^{7}$$

Expand

$$-x^{5}y^{7}$$

Solution Steps

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

$$8x^{2}y\left(-\frac{1}{2}\right)^{3}x^{3}\left(y^{2}\right)^{3}$$

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

$$8x^{2}y\left(-\frac{1}{2}\right)^{3}x^{3}y^{6}$$

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

$$8x^{2}y\left(-\frac{1}{8}\right)x^{3}y^{6}$$

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

$$-x^{2}yx^{3}y^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-x^{5}yy^{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$-x^{5}y^{7}$$