Solve (5x^4y^5/10xy^-2)^3

$$( \frac { 5 x ^ { 4 } y ^ { 5 } } { 10 x y ^ { - 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{x^{9}y^{21}}{8}$$

Solution Steps

Cancel out 5x in both numerator and denominator.

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

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

$$\left(\frac{x^{3}y^{7}}{2}\right)^{3}$$

To raise \frac{x^{3}y^{7}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{3}y^{7}\right)^{3}}{2^{3}}$$

Expand \left(x^{3}y^{7}\right)^{3}.

$$\frac{\left(x^{3}\right)^{3}\left(y^{7}\right)^{3}}{2^{3}}$$

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

$$\frac{x^{9}\left(y^{7}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{x^{9}y^{21}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{9}y^{21}}{8}$$

Expand

$$\frac{x^{9}y^{21}}{8}$$

Solution Steps

Cancel out 5x in both numerator and denominator.

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

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

$$\left(\frac{x^{3}y^{7}}{2}\right)^{3}$$

To raise \frac{x^{3}y^{7}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{3}y^{7}\right)^{3}}{2^{3}}$$

Expand \left(x^{3}y^{7}\right)^{3}.

$$\frac{\left(x^{3}\right)^{3}\left(y^{7}\right)^{3}}{2^{3}}$$

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

$$\frac{x^{9}\left(y^{7}\right)^{3}}{2^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{x^{9}y^{21}}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{x^{9}y^{21}}{8}$$