Solve (5x^-2y^3/2xy^2)^3=

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

Evaluate

$$\frac{125y^{3}}{8x^{9}}$$

Solution Steps

Cancel out y^{2} in both numerator and denominator.

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

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

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

To raise \frac{5y}{2x^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(5y\right)^{3}.

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

Calculate 5 to the power of 3 and get 125.

$$\frac{125y^{3}}{\left(2x^{3}\right)^{3}}$$

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

$$\frac{125y^{3}}{2^{3}\left(x^{3}\right)^{3}}$$

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

$$\frac{125y^{3}}{2^{3}x^{9}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{125y^{3}}{8x^{9}}$$

Expand

$$\frac{125y^{3}}{8x^{9}}$$

Solution Steps

Cancel out y^{2} in both numerator and denominator.

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

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

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

To raise \frac{5y}{2x^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(5y\right)^{3}.

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

Calculate 5 to the power of 3 and get 125.

$$\frac{125y^{3}}{\left(2x^{3}\right)^{3}}$$

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

$$\frac{125y^{3}}{2^{3}\left(x^{3}\right)^{3}}$$

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

$$\frac{125y^{3}}{2^{3}x^{9}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{125y^{3}}{8x^{9}}$$