Solve {left(2x^-3y^5w^-2/3y^7{x^-4{w}^-4}right)}^-3

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

Evaluate

$$\frac{27\times \left(\frac{y}{w}\right)^{6}}{8x^{3}}$$

Solution Steps

Cancel out y^{5} in both numerator and denominator.

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

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

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

Calculate x to the power of 1 and get x.

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

To raise \frac{2xw^{2}}{3y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{\left(3y^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{3^{-3}\left(y^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{3^{-3}y^{-6}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{\frac{1}{27}y^{-6}}$$

Expand

$$\frac{27\times \left(\frac{y}{w}\right)^{6}}{8x^{3}}$$

Solution Steps

Cancel out y^{5} in both numerator and denominator.

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

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

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

Calculate x to the power of 1 and get x.

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

To raise \frac{2xw^{2}}{3y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{\left(3y^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{3^{-3}\left(y^{2}\right)^{-3}}$$

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

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{3^{-3}y^{-6}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{8}x^{-3}w^{-6}}{\frac{1}{27}y^{-6}}$$