Solve [(-3x^{2}y^{4})^{2}*x^{3}-2x*(3x^{2}y^{2})^3*1/2y^2]div9x^7y^8

$$[ ( - 3 x ^ { 2 } y ^ { 4 } ) ^ { 2 } \cdot x ^ { 3 } - 2 x \cdot ( 3 x ^ { 2 } y ^ { 2 } ) ^ { 3 } \cdot \frac { 1 } { 2 } y ^ { 2 } ] \div 9 x ^ { 7 } y ^ { 8 }$$

Evaluate

$$-2x^{14}y^{16}$$

Solution Steps

Expand \left(-3x^{2}y^{4}\right)^{2}.

$$\frac{\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{4}\right)^{2}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{\left(-3\right)^{2}x^{4}\left(y^{4}\right)^{2}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(-3\right)^{2}x^{4}y^{8}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9x^{4}y^{8}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{9x^{7}y^{8}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Expand \left(3x^{2}y^{2}\right)^{3}.

$$\frac{9x^{7}y^{8}-2x\times 3^{3}\left(x^{2}\right)^{3}\left(y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-2x\times 3^{3}x^{6}\left(y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-2x\times 3^{3}x^{6}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{9x^{7}y^{8}-2x\times 27x^{6}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Multiply 2 and 27 to get 54.

$$\frac{9x^{7}y^{8}-54xx^{6}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-54x^{7}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Multiply 54 and \frac{1}{2} to get 27.

$$\frac{9x^{7}y^{8}-27x^{7}y^{6}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-27x^{7}y^{8}}{9}x^{7}y^{8}$$

Combine 9x^{7}y^{8} and -27x^{7}y^{8} to get -18x^{7}y^{8}.

$$\frac{-18x^{7}y^{8}}{9}x^{7}y^{8}$$

Divide -18x^{7}y^{8} by 9 to get -2x^{7}y^{8}.

$$-2x^{7}y^{8}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$-2x^{14}y^{8}y^{8}$$

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$-2x^{14}y^{16}$$

Expand

$$-2x^{14}y^{16}$$

Solution Steps

Expand \left(-3x^{2}y^{4}\right)^{2}.

$$\frac{\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{4}\right)^{2}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{\left(-3\right)^{2}x^{4}\left(y^{4}\right)^{2}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(-3\right)^{2}x^{4}y^{8}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{9x^{4}y^{8}x^{3}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{9x^{7}y^{8}-2x\times \left(3x^{2}y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Expand \left(3x^{2}y^{2}\right)^{3}.

$$\frac{9x^{7}y^{8}-2x\times 3^{3}\left(x^{2}\right)^{3}\left(y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-2x\times 3^{3}x^{6}\left(y^{2}\right)^{3}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-2x\times 3^{3}x^{6}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{9x^{7}y^{8}-2x\times 27x^{6}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Multiply 2 and 27 to get 54.

$$\frac{9x^{7}y^{8}-54xx^{6}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-54x^{7}y^{6}\times \frac{1}{2}y^{2}}{9}x^{7}y^{8}$$

Multiply 54 and \frac{1}{2} to get 27.

$$\frac{9x^{7}y^{8}-27x^{7}y^{6}y^{2}}{9}x^{7}y^{8}$$

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

$$\frac{9x^{7}y^{8}-27x^{7}y^{8}}{9}x^{7}y^{8}$$

Combine 9x^{7}y^{8} and -27x^{7}y^{8} to get -18x^{7}y^{8}.

$$\frac{-18x^{7}y^{8}}{9}x^{7}y^{8}$$

Divide -18x^{7}y^{8} by 9 to get -2x^{7}y^{8}.

$$-2x^{7}y^{8}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$-2x^{14}y^{8}y^{8}$$

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$-2x^{14}y^{16}$$