Solve (frac{4xy^{3}}{7})^{2}x(frac{x^{2}y}{2})^3x(z^3/xy^3)^4

$$( \frac { 4 x y ^ { 3 } } { 7 } ) ^ { 2 } x ( \frac { x ^ { 2 } y } { 2 } ) ^ { 3 } x ( \frac { z ^ { 3 } } { x y ^ { 3 } } ) ^ { 4 }$$

Evaluate

$$\frac{2x^{6}z^{12}}{49y^{3}}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\left(\frac{4xy^{3}}{7}\right)^{2}x^{2}\times \left(\frac{x^{2}y}{2}\right)^{3}\times \left(\frac{z^{3}}{xy^{3}}\right)^{4}$$

To raise \frac{4xy^{3}}{7} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2}\times \left(\frac{x^{2}y}{2}\right)^{3}\times \left(\frac{z^{3}}{xy^{3}}\right)^{4}$$

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

$$\frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2}\times \frac{\left(x^{2}y\right)^{3}}{2^{3}}\times \left(\frac{z^{3}}{xy^{3}}\right)^{4}$$

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

$$\frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2}\times \frac{\left(x^{2}y\right)^{3}}{2^{3}}\times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}}$$

Express \frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2} as a single fraction.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}}{7^{2}}\times \frac{\left(x^{2}y\right)^{3}}{2^{3}}\times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}}$$

Multiply \frac{\left(4xy^{3}\right)^{2}x^{2}}{7^{2}} times \frac{\left(x^{2}y\right)^{3}}{2^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}}{7^{2}\times 2^{3}}\times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}}$$

Multiply \frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}}{7^{2}\times 2^{3}} times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}\left(z^{3}\right)^{4}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

Expand \left(4xy^{3}\right)^{2}.

$$\frac{4^{2}x^{2}\left(y^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

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

$$\frac{4^{2}x^{2}y^{6}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{2}y^{6}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{16x^{4}y^{6}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

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

$$\frac{16x^{4}y^{6}\left(x^{2}\right)^{3}y^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

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

$$\frac{16x^{4}y^{6}x^{6}y^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{16x^{10}y^{6}y^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{16x^{10}y^{9}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{16x^{10}y^{9}z^{12}}{49\times 2^{3}\left(xy^{3}\right)^{4}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{16x^{10}y^{9}z^{12}}{49\times 8\left(xy^{3}\right)^{4}}$$

Multiply 49 and 8 to get 392.

$$\frac{16x^{10}y^{9}z^{12}}{392\left(xy^{3}\right)^{4}}$$

Expand \left(xy^{3}\right)^{4}.

$$\frac{16x^{10}y^{9}z^{12}}{392x^{4}\left(y^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{16x^{10}y^{9}z^{12}}{392x^{4}y^{12}}$$

Cancel out 8x^{4}y^{9} in both numerator and denominator.

$$\frac{2x^{6}z^{12}}{49y^{3}}$$

Expand

$$\frac{2x^{6}z^{12}}{49y^{3}}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\left(\frac{4xy^{3}}{7}\right)^{2}x^{2}\times \left(\frac{x^{2}y}{2}\right)^{3}\times \left(\frac{z^{3}}{xy^{3}}\right)^{4}$$

To raise \frac{4xy^{3}}{7} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2}\times \left(\frac{x^{2}y}{2}\right)^{3}\times \left(\frac{z^{3}}{xy^{3}}\right)^{4}$$

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

$$\frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2}\times \frac{\left(x^{2}y\right)^{3}}{2^{3}}\times \left(\frac{z^{3}}{xy^{3}}\right)^{4}$$

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

$$\frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2}\times \frac{\left(x^{2}y\right)^{3}}{2^{3}}\times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}}$$

Express \frac{\left(4xy^{3}\right)^{2}}{7^{2}}x^{2} as a single fraction.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}}{7^{2}}\times \frac{\left(x^{2}y\right)^{3}}{2^{3}}\times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}}$$

Multiply \frac{\left(4xy^{3}\right)^{2}x^{2}}{7^{2}} times \frac{\left(x^{2}y\right)^{3}}{2^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}}{7^{2}\times 2^{3}}\times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}}$$

Multiply \frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}}{7^{2}\times 2^{3}} times \frac{\left(z^{3}\right)^{4}}{\left(xy^{3}\right)^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}\left(z^{3}\right)^{4}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(4xy^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

Expand \left(4xy^{3}\right)^{2}.

$$\frac{4^{2}x^{2}\left(y^{3}\right)^{2}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

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

$$\frac{4^{2}x^{2}y^{6}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{2}y^{6}x^{2}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{16x^{4}y^{6}\left(x^{2}y\right)^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

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

$$\frac{16x^{4}y^{6}\left(x^{2}\right)^{3}y^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

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

$$\frac{16x^{4}y^{6}x^{6}y^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{16x^{10}y^{6}y^{3}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{16x^{10}y^{9}z^{12}}{7^{2}\times 2^{3}\left(xy^{3}\right)^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{16x^{10}y^{9}z^{12}}{49\times 2^{3}\left(xy^{3}\right)^{4}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{16x^{10}y^{9}z^{12}}{49\times 8\left(xy^{3}\right)^{4}}$$

Multiply 49 and 8 to get 392.

$$\frac{16x^{10}y^{9}z^{12}}{392\left(xy^{3}\right)^{4}}$$

Expand \left(xy^{3}\right)^{4}.

$$\frac{16x^{10}y^{9}z^{12}}{392x^{4}\left(y^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{16x^{10}y^{9}z^{12}}{392x^{4}y^{12}}$$

Cancel out 8x^{4}y^{9} in both numerator and denominator.

$$\frac{2x^{6}z^{12}}{49y^{3}}$$