Solve [4/3x^{2}y^3]^3[3/16x^5]^2

$$[ \frac { 4 } { 3 } x ^ { 2 } y ^ { 3 } ] ^ { 3 } [ \frac { 3 } { 16 x ^ { 5 } } ] ^ { 2 }$$

Evaluate

$$\frac{y^{9}}{12x^{4}}$$

Solution Steps

Expand \left(\frac{4}{3}x^{2}y^{3}\right)^{3}.

$$\left(\frac{4}{3}\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{4}{3}\right)^{3}x^{6}\left(y^{3}\right)^{3}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

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

$$\left(\frac{4}{3}\right)^{3}x^{6}y^{9}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

Calculate \frac{4}{3} to the power of 3 and get \frac{64}{27}.

$$\frac{64}{27}x^{6}y^{9}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

To raise \frac{3}{16x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{64}{27}x^{6}y^{9}\times \frac{3^{2}}{\left(16x^{5}\right)^{2}}$$

Multiply \frac{64}{27} times \frac{3^{2}}{\left(16x^{5}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 3^{2}}{27\times \left(16x^{5}\right)^{2}}x^{6}y^{9}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{64\times 9}{27\times \left(16x^{5}\right)^{2}}x^{6}y^{9}$$

Multiply 64 and 9 to get 576.

$$\frac{576}{27\times \left(16x^{5}\right)^{2}}x^{6}y^{9}$$

Expand \left(16x^{5}\right)^{2}.

$$\frac{576}{27\times 16^{2}\left(x^{5}\right)^{2}}x^{6}y^{9}$$

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

$$\frac{576}{27\times 16^{2}x^{10}}x^{6}y^{9}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{576}{27\times 256x^{10}}x^{6}y^{9}$$

Multiply 27 and 256 to get 6912.

$$\frac{576}{6912x^{10}}x^{6}y^{9}$$

Express \frac{576}{6912x^{10}}x^{6} as a single fraction.

$$\frac{576x^{6}}{6912x^{10}}y^{9}$$

Cancel out 576x^{6} in both numerator and denominator.

$$\frac{1}{12x^{4}}y^{9}$$

Express \frac{1}{12x^{4}}y^{9} as a single fraction.

$$\frac{y^{9}}{12x^{4}}$$

Expand

$$\frac{y^{9}}{12x^{4}}$$

Solution Steps

Expand \left(\frac{4}{3}x^{2}y^{3}\right)^{3}.

$$\left(\frac{4}{3}\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{4}{3}\right)^{3}x^{6}\left(y^{3}\right)^{3}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

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

$$\left(\frac{4}{3}\right)^{3}x^{6}y^{9}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

Calculate \frac{4}{3} to the power of 3 and get \frac{64}{27}.

$$\frac{64}{27}x^{6}y^{9}\times \left(\frac{3}{16x^{5}}\right)^{2}$$

To raise \frac{3}{16x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{64}{27}x^{6}y^{9}\times \frac{3^{2}}{\left(16x^{5}\right)^{2}}$$

Multiply \frac{64}{27} times \frac{3^{2}}{\left(16x^{5}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 3^{2}}{27\times \left(16x^{5}\right)^{2}}x^{6}y^{9}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{64\times 9}{27\times \left(16x^{5}\right)^{2}}x^{6}y^{9}$$

Multiply 64 and 9 to get 576.

$$\frac{576}{27\times \left(16x^{5}\right)^{2}}x^{6}y^{9}$$

Expand \left(16x^{5}\right)^{2}.

$$\frac{576}{27\times 16^{2}\left(x^{5}\right)^{2}}x^{6}y^{9}$$

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

$$\frac{576}{27\times 16^{2}x^{10}}x^{6}y^{9}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{576}{27\times 256x^{10}}x^{6}y^{9}$$

Multiply 27 and 256 to get 6912.

$$\frac{576}{6912x^{10}}x^{6}y^{9}$$

Express \frac{576}{6912x^{10}}x^{6} as a single fraction.

$$\frac{576x^{6}}{6912x^{10}}y^{9}$$

Cancel out 576x^{6} in both numerator and denominator.

$$\frac{1}{12x^{4}}y^{9}$$

Express \frac{1}{12x^{4}}y^{9} as a single fraction.

$$\frac{y^{9}}{12x^{4}}$$