Solve (frac{3x^{0}y^{3}}{4})^3div(3x^-2y^5/2)^2

$$( \frac { 3 x ^ { 0 } y ^ { 3 } } { 4 } ) ^ { 3 } \div ( \frac { 3 x ^ { - 2 } y ^ { 5 } } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{3x^{4}}{16y}$$

Solution Steps

Calculate x to the power of 0 and get 1.

$$\frac{\left(\frac{3\times 1y^{3}}{4}\right)^{3}}{\left(\frac{3x^{-2}y^{5}}{2}\right)^{2}}$$

Multiply 3 and 1 to get 3.

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

To raise \frac{3y^{3}}{4} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Divide \frac{\left(3y^{3}\right)^{3}}{4^{3}} by \frac{\left(3x^{-2}y^{5}\right)^{2}}{2^{2}} by multiplying \frac{\left(3y^{3}\right)^{3}}{4^{3}} by the reciprocal of \frac{\left(3x^{-2}y^{5}\right)^{2}}{2^{2}}.

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

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

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

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

$$\frac{3^{3}y^{9}\times 2^{2}}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27y^{9}\times 2^{2}}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{27y^{9}\times 4}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Multiply 27 and 4 to get 108.

$$\frac{108y^{9}}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{108y^{9}}{64\times \left(3x^{-2}y^{5}\right)^{2}}$$

Expand \left(3x^{-2}y^{5}\right)^{2}.

$$\frac{108y^{9}}{64\times 3^{2}\left(x^{-2}\right)^{2}\left(y^{5}\right)^{2}}$$

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

$$\frac{108y^{9}}{64\times 3^{2}x^{-4}\left(y^{5}\right)^{2}}$$

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

$$\frac{108y^{9}}{64\times 3^{2}x^{-4}y^{10}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{108y^{9}}{64\times 9x^{-4}y^{10}}$$

Multiply 64 and 9 to get 576.

$$\frac{108y^{9}}{576x^{-4}y^{10}}$$

Cancel out 36y^{9} in both numerator and denominator.

$$\frac{3}{16x^{-4}y}$$

Expand

$$\frac{3x^{4}}{16y}$$

Solution Steps

Calculate x to the power of 0 and get 1.

$$\frac{\left(\frac{3\times 1y^{3}}{4}\right)^{3}}{\left(\frac{3x^{-2}y^{5}}{2}\right)^{2}}$$

Multiply 3 and 1 to get 3.

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

To raise \frac{3y^{3}}{4} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Divide \frac{\left(3y^{3}\right)^{3}}{4^{3}} by \frac{\left(3x^{-2}y^{5}\right)^{2}}{2^{2}} by multiplying \frac{\left(3y^{3}\right)^{3}}{4^{3}} by the reciprocal of \frac{\left(3x^{-2}y^{5}\right)^{2}}{2^{2}}.

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

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

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

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

$$\frac{3^{3}y^{9}\times 2^{2}}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27y^{9}\times 2^{2}}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{27y^{9}\times 4}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Multiply 27 and 4 to get 108.

$$\frac{108y^{9}}{4^{3}\times \left(3x^{-2}y^{5}\right)^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{108y^{9}}{64\times \left(3x^{-2}y^{5}\right)^{2}}$$

Expand \left(3x^{-2}y^{5}\right)^{2}.

$$\frac{108y^{9}}{64\times 3^{2}\left(x^{-2}\right)^{2}\left(y^{5}\right)^{2}}$$

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

$$\frac{108y^{9}}{64\times 3^{2}x^{-4}\left(y^{5}\right)^{2}}$$

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

$$\frac{108y^{9}}{64\times 3^{2}x^{-4}y^{10}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{108y^{9}}{64\times 9x^{-4}y^{10}}$$

Multiply 64 and 9 to get 576.

$$\frac{108y^{9}}{576x^{-4}y^{10}}$$

Cancel out 36y^{9} in both numerator and denominator.

$$\frac{3}{16x^{-4}y}$$