Solve 49/9{(3/7x^{2}y^{2})^{12}:[(3/7x^{2}y^{2})^{2}]^{5}*(3/7x^{2}y^{2})}-x^{3}y^{2}(frac{9}{14}x^3y^4-frac{5}{7}x^3y^4)=

$$\frac { 49 } { 9 } \{ ( \frac { 3 } { 7 } x ^ { 2 } y ^ { 2 } ) ^ { 12 } : [ ( \frac { 3 } { 7 } x ^ { 2 } y ^ { 2 } ) ^ { 2 } ] ^ { 5 } \cdot ( \frac { 3 } { 7 } x ^ { 2 } y ^ { 2 } ) \} - x ^ { 3 } y ^ { 2 } ( \frac { 9 } { 14 } x ^ { 3 } y ^ { 4 } - \frac { 5 } { 7 } x ^ { 3 } y ^ { 4 } ) =$$

Evaluate

$$\frac{\left(xy\right)^{6}}{2}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{49}{9}\times \frac{\left(\frac{3}{7}x^{2}y^{2}\right)^{12}}{\left(\frac{3}{7}x^{2}y^{2}\right)^{10}}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 12 to get 2.

$$\frac{49}{9}\times \left(\frac{3}{7}x^{2}y^{2}\right)^{2}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Expand \left(\frac{3}{7}x^{2}y^{2}\right)^{2}.

$$\frac{49}{9}\times \left(\frac{3}{7}\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

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

$$\frac{49}{9}\times \left(\frac{3}{7}\right)^{2}x^{4}\left(y^{2}\right)^{2}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

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

$$\frac{49}{9}\times \left(\frac{3}{7}\right)^{2}x^{4}y^{4}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$\frac{49}{9}\times \frac{9}{49}x^{4}y^{4}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Multiply \frac{49}{9} and \frac{9}{49} to get 1.

$$x^{4}y^{4}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$x^{6}y^{4}\times \frac{3}{7}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$x^{6}y^{6}\times \frac{3}{7}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Combine \frac{9}{14}x^{3}y^{4} and -\frac{5}{7}x^{3}y^{4} to get -\frac{1}{14}x^{3}y^{4}.

$$x^{6}y^{6}\times \frac{3}{7}-x^{3}y^{2}\left(-\frac{1}{14}\right)x^{3}y^{4}$$

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

$$x^{6}y^{6}\times \frac{3}{7}-x^{6}y^{2}\left(-\frac{1}{14}\right)y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$x^{6}y^{6}\times \frac{3}{7}-x^{6}y^{6}\left(-\frac{1}{14}\right)$$

Combine x^{6}y^{6}\times \frac{3}{7} and -x^{6}y^{6}\left(-\frac{1}{14}\right) to get \frac{1}{2}x^{6}y^{6}.

$$\frac{1}{2}x^{6}y^{6}$$

Expand

$$\frac{\left(xy\right)^{6}}{2}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{49}{9}\times \frac{\left(\frac{3}{7}x^{2}y^{2}\right)^{12}}{\left(\frac{3}{7}x^{2}y^{2}\right)^{10}}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 12 to get 2.

$$\frac{49}{9}\times \left(\frac{3}{7}x^{2}y^{2}\right)^{2}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Expand \left(\frac{3}{7}x^{2}y^{2}\right)^{2}.

$$\frac{49}{9}\times \left(\frac{3}{7}\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

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

$$\frac{49}{9}\times \left(\frac{3}{7}\right)^{2}x^{4}\left(y^{2}\right)^{2}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

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

$$\frac{49}{9}\times \left(\frac{3}{7}\right)^{2}x^{4}y^{4}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$\frac{49}{9}\times \frac{9}{49}x^{4}y^{4}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Multiply \frac{49}{9} and \frac{9}{49} to get 1.

$$x^{4}y^{4}\times \frac{3}{7}x^{2}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$x^{6}y^{4}\times \frac{3}{7}y^{2}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$x^{6}y^{6}\times \frac{3}{7}-x^{3}y^{2}\left(\frac{9}{14}x^{3}y^{4}-\frac{5}{7}x^{3}y^{4}\right)$$

Combine \frac{9}{14}x^{3}y^{4} and -\frac{5}{7}x^{3}y^{4} to get -\frac{1}{14}x^{3}y^{4}.

$$x^{6}y^{6}\times \frac{3}{7}-x^{3}y^{2}\left(-\frac{1}{14}\right)x^{3}y^{4}$$

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

$$x^{6}y^{6}\times \frac{3}{7}-x^{6}y^{2}\left(-\frac{1}{14}\right)y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$x^{6}y^{6}\times \frac{3}{7}-x^{6}y^{6}\left(-\frac{1}{14}\right)$$

Combine x^{6}y^{6}\times \frac{3}{7} and -x^{6}y^{6}\left(-\frac{1}{14}\right) to get \frac{1}{2}x^{6}y^{6}.

$$\frac{1}{2}x^{6}y^{6}$$