Solve {left(x^3y^-2/x^-2y^6right)}^4

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

Evaluate

$$\frac{x^{20}}{y^{32}}$$

Solution Steps

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

$$\left(\frac{y^{-2}x^{5}}{y^{6}}\right)^{4}$$

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

$$\left(\frac{x^{5}}{y^{8}}\right)^{4}$$

To raise \frac{x^{5}}{y^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{5}\right)^{4}}{\left(y^{8}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{x^{20}}{\left(y^{8}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 4 to get 32.

$$\frac{x^{20}}{y^{32}}$$

Expand

$$\frac{x^{20}}{y^{32}}$$

Solution Steps

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

$$\left(\frac{y^{-2}x^{5}}{y^{6}}\right)^{4}$$

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

$$\left(\frac{x^{5}}{y^{8}}\right)^{4}$$

To raise \frac{x^{5}}{y^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{5}\right)^{4}}{\left(y^{8}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{x^{20}}{\left(y^{8}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 4 to get 32.

$$\frac{x^{20}}{y^{32}}$$