Solve (frac{x^{4}y^{7}}{x^{7}y^{10}})(frac{x^{-5}y^-7}{x^-3y^-5})^2

$$( \frac { x ^ { 4 } y ^ { 7 } } { x ^ { 7 } y ^ { 10 } } ) ( \frac { x ^ { - 5 } y ^ { - 7 } } { x ^ { - 3 } y ^ { - 5 } } ) ^ { 2 }$$

Evaluate

$$\frac{1}{\left(xy\right)^{7}}$$

Solution Steps

Cancel out x^{4}y^{7} in both numerator and denominator.

$$\frac{1}{x^{3}y^{3}}\times \left(\frac{x^{-5}y^{-7}}{x^{-3}y^{-5}}\right)^{2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

To raise \frac{1}{x^{2}y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{1}{x^{3}y^{3}} times \frac{1^{2}}{\left(x^{2}y^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

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

$$\frac{1}{x^{3}y^{3}x^{4}\left(y^{2}\right)^{2}}$$

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

$$\frac{1}{x^{3}y^{3}x^{4}y^{4}}$$

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

$$\frac{1}{x^{7}y^{3}y^{4}}$$

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

$$\frac{1}{x^{7}y^{7}}$$

Expand

$$\frac{1}{\left(xy\right)^{7}}$$

Solution Steps

Cancel out x^{4}y^{7} in both numerator and denominator.

$$\frac{1}{x^{3}y^{3}}\times \left(\frac{x^{-5}y^{-7}}{x^{-3}y^{-5}}\right)^{2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

To raise \frac{1}{x^{2}y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{1}{x^{3}y^{3}} times \frac{1^{2}}{\left(x^{2}y^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

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

$$\frac{1}{x^{3}y^{3}x^{4}\left(y^{2}\right)^{2}}$$

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

$$\frac{1}{x^{3}y^{3}x^{4}y^{4}}$$

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

$$\frac{1}{x^{7}y^{3}y^{4}}$$

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

$$\frac{1}{x^{7}y^{7}}$$