Solve x^-4(x^5/y^-2)^3

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

Evaluate

$$y^{6}x^{11}$$

Solution Steps

To raise \frac{x^{5}}{y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

Express x^{-4}\times \frac{\left(x^{5}\right)^{3}}{\left(y^{-2}\right)^{3}} as a single fraction.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{x^{-4}x^{15}}{\left(y^{-2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add -4 and 15 to get 11.

$$\frac{x^{11}}{\left(y^{-2}\right)^{3}}$$

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

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

Expand

$$y^{6}x^{11}$$

Solution Steps

To raise \frac{x^{5}}{y^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

Express x^{-4}\times \frac{\left(x^{5}\right)^{3}}{\left(y^{-2}\right)^{3}} as a single fraction.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{x^{-4}x^{15}}{\left(y^{-2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add -4 and 15 to get 11.

$$\frac{x^{11}}{\left(y^{-2}\right)^{3}}$$

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

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