Solve (3xy^5/6x^-4y)^2=

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

Evaluate

$$\frac{y^{8}x^{10}}{4}$$

Solution Steps

Cancel out 3y in both numerator and denominator.

$$\left(\frac{xy^{4}}{2x^{-4}}\right)^{2}$$

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

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

To raise \frac{y^{4}x^{5}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(y^{4}x^{5}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{y^{8}\left(x^{5}\right)^{2}}{2^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{y^{8}x^{10}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{y^{8}x^{10}}{4}$$

Expand

$$\frac{y^{8}x^{10}}{4}$$

Solution Steps

Cancel out 3y in both numerator and denominator.

$$\left(\frac{xy^{4}}{2x^{-4}}\right)^{2}$$

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

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

To raise \frac{y^{4}x^{5}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(y^{4}x^{5}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{y^{8}\left(x^{5}\right)^{2}}{2^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{y^{8}x^{10}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{y^{8}x^{10}}{4}$$