Solve (frac{x^{6}y^{3}}{x^{3}y^-3}*y^-7/x^-3)^10

$$( \frac { x ^ { 6 } y ^ { 3 } } { x ^ { 3 } y ^ { - 3 } } \cdot \frac { y ^ { - 7 } } { x ^ { - 3 } } ) ^ { 10 }$$

Evaluate

$$\frac{x^{60}}{y^{10}}$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$\left(\frac{x^{3}y^{3}}{y^{-3}}\times \frac{y^{-7}}{x^{-3}}\right)^{10}$$

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

$$\left(x^{3}y^{6}\times \frac{y^{-7}}{x^{-3}}\right)^{10}$$

Express x^{3}\times \frac{y^{-7}}{x^{-3}} as a single fraction.

$$\left(\frac{x^{3}y^{-7}}{x^{-3}}y^{6}\right)^{10}$$

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

$$\left(y^{-7}x^{6}y^{6}\right)^{10}$$

Expand \left(y^{-7}x^{6}y^{6}\right)^{10}.

$$\left(y^{-7}\right)^{10}\left(x^{6}\right)^{10}\left(y^{6}\right)^{10}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 10 to get -70.

$$y^{-70}\left(x^{6}\right)^{10}\left(y^{6}\right)^{10}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 10 to get 60.

$$y^{-70}x^{60}\left(y^{6}\right)^{10}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 10 to get 60.

$$y^{-70}x^{60}y^{60}$$

To multiply powers of the same base, add their exponents. Add -70 and 60 to get -10.

$$y^{-10}x^{60}$$

Expand

$$\frac{x^{60}}{y^{10}}$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$\left(\frac{x^{3}y^{3}}{y^{-3}}\times \frac{y^{-7}}{x^{-3}}\right)^{10}$$

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

$$\left(x^{3}y^{6}\times \frac{y^{-7}}{x^{-3}}\right)^{10}$$

Express x^{3}\times \frac{y^{-7}}{x^{-3}} as a single fraction.

$$\left(\frac{x^{3}y^{-7}}{x^{-3}}y^{6}\right)^{10}$$

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

$$\left(y^{-7}x^{6}y^{6}\right)^{10}$$

Expand \left(y^{-7}x^{6}y^{6}\right)^{10}.

$$\left(y^{-7}\right)^{10}\left(x^{6}\right)^{10}\left(y^{6}\right)^{10}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 10 to get -70.

$$y^{-70}\left(x^{6}\right)^{10}\left(y^{6}\right)^{10}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 10 to get 60.

$$y^{-70}x^{60}\left(y^{6}\right)^{10}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 10 to get 60.

$$y^{-70}x^{60}y^{60}$$

To multiply powers of the same base, add their exponents. Add -70 and 60 to get -10.

$$y^{-10}x^{60}$$