Solve 7x^2ydiv16/3x^6y^2*(-2xy)^3

$$7 x ^ { 2 } y \div \frac { 16 } { 3 } x ^ { 6 } y ^ { 2 } \times ( - 2 x y ) ^ { 3 }$$

Evaluate

$$-\frac{21y^{6}x^{11}}{2}$$

Solution Steps

Divide 7x^{2}y by \frac{16}{3} by multiplying 7x^{2}y by the reciprocal of \frac{16}{3}.

$$\frac{7x^{2}y\times 3}{16}x^{6}y^{2}\left(-2xy\right)^{3}$$

Multiply 7 and 3 to get 21.

$$\frac{21x^{2}y}{16}x^{6}y^{2}\left(-2xy\right)^{3}$$

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

$$\frac{21x^{2}y}{16}x^{6}y^{2}\left(-2\right)^{3}x^{3}y^{3}$$

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

$$\frac{21x^{2}y}{16}x^{6}y^{2}\left(-8\right)x^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{21x^{2}y}{16}x^{9}y^{2}\left(-8\right)y^{3}$$

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

$$\frac{21x^{2}y}{16}x^{9}y^{5}\left(-8\right)$$

Express \frac{21x^{2}y}{16}x^{9} as a single fraction.

$$\frac{21x^{2}yx^{9}}{16}y^{5}\left(-8\right)$$

Express \frac{21x^{2}yx^{9}}{16}y^{5} as a single fraction.

$$\frac{21x^{2}yx^{9}y^{5}}{16}\left(-8\right)$$

Cancel out 16, the greatest common factor in 8 and 16.

$$\frac{21x^{2}yx^{9}y^{5}}{-2}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$\frac{21x^{11}yy^{5}}{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{21x^{11}y^{6}}{-2}$$

Expand

$$-\frac{21y^{6}x^{11}}{2}$$

Solution Steps

Divide 7x^{2}y by \frac{16}{3} by multiplying 7x^{2}y by the reciprocal of \frac{16}{3}.

$$\frac{7x^{2}y\times 3}{16}x^{6}y^{2}\left(-2xy\right)^{3}$$

Multiply 7 and 3 to get 21.

$$\frac{21x^{2}y}{16}x^{6}y^{2}\left(-2xy\right)^{3}$$

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

$$\frac{21x^{2}y}{16}x^{6}y^{2}\left(-2\right)^{3}x^{3}y^{3}$$

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

$$\frac{21x^{2}y}{16}x^{6}y^{2}\left(-8\right)x^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{21x^{2}y}{16}x^{9}y^{2}\left(-8\right)y^{3}$$

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

$$\frac{21x^{2}y}{16}x^{9}y^{5}\left(-8\right)$$

Express \frac{21x^{2}y}{16}x^{9} as a single fraction.

$$\frac{21x^{2}yx^{9}}{16}y^{5}\left(-8\right)$$

Express \frac{21x^{2}yx^{9}}{16}y^{5} as a single fraction.

$$\frac{21x^{2}yx^{9}y^{5}}{16}\left(-8\right)$$

Cancel out 16, the greatest common factor in 8 and 16.

$$\frac{21x^{2}yx^{9}y^{5}}{-2}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$\frac{21x^{11}yy^{5}}{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{21x^{11}y^{6}}{-2}$$