Solve ({left(2x^-4y^5/4x^-2y^-1right)}^-3

$$( { \left( \frac{ 2 { x }^{ -4 } { y }^{ 5 } }{ 4 { x }^{ -2 } { y }^{ -1 } } \right) }^{ -3 }$$

Evaluate

$$\frac{8x^{6}}{y^{18}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(\frac{x^{-4}y^{5}}{2x^{-2}\times \frac{1}{y}}\right)^{-3}$$

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

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

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

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

To raise \frac{y^{6}}{2x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{y^{-18}}{\left(2x^{2}\right)^{-3}}$$

Expand \left(2x^{2}\right)^{-3}.

$$\frac{y^{-18}}{2^{-3}\left(x^{2}\right)^{-3}}$$

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

$$\frac{y^{-18}}{2^{-3}x^{-6}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{y^{-18}}{\frac{1}{8}x^{-6}}$$

Expand

$$\frac{8x^{6}}{y^{18}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(\frac{x^{-4}y^{5}}{2x^{-2}\times \frac{1}{y}}\right)^{-3}$$

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

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

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

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

To raise \frac{y^{6}}{2x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{y^{-18}}{\left(2x^{2}\right)^{-3}}$$

Expand \left(2x^{2}\right)^{-3}.

$$\frac{y^{-18}}{2^{-3}\left(x^{2}\right)^{-3}}$$

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

$$\frac{y^{-18}}{2^{-3}x^{-6}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{y^{-18}}{\frac{1}{8}x^{-6}}$$