Solve {left(x^-5y^3/2x^-4y^6right)}^3

$${ \left( \frac{ { x }^{ -5 } { y }^{ 3 } }{ 2 { x }^{ -4 } { y }^{ 6 } } \right) }^{ 3 }$$

Evaluate

$$\frac{1}{8x^{3}y^{9}}$$

Solution Steps

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

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

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

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

Calculate x to the power of 1 and get x.

$$\left(\frac{1}{2xy^{3}}\right)^{3}$$

To raise \frac{1}{2xy^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(2xy^{3}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(2xy^{3}\right)^{3}}$$

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{1}{2^{3}x^{3}y^{9}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{8x^{3}y^{9}}$$

Expand

$$\frac{1}{8x^{3}y^{9}}$$

Solution Steps

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

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

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

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

Calculate x to the power of 1 and get x.

$$\left(\frac{1}{2xy^{3}}\right)^{3}$$

To raise \frac{1}{2xy^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(2xy^{3}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(2xy^{3}\right)^{3}}$$

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{1}{2^{3}x^{3}y^{9}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{8x^{3}y^{9}}$$