Solve frac{(3x^{2})^{2}}{4yz}*4xy^3/7z^2div8yz^2/x^2=

$$\frac { ( 3 x ^ { 2 } ) ^ { 2 } } { 4 y z } \times \frac { 4 x y ^ { 3 } } { 7 z ^ { 2 } } \div \frac { 8 y z ^ { 2 } } { x ^ { 2 } } =$$

Evaluate

$$\frac{9yx^{7}}{56z^{5}}$$

Short Solution Steps

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

$$\frac{\frac{3^{2}\left(x^{2}\right)^{2}}{4yz}\times \frac{4xy^{3}}{7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

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

$$\frac{\frac{3^{2}x^{4}}{4yz}\times \frac{4xy^{3}}{7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{9x^{4}}{4yz}\times \frac{4xy^{3}}{7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Multiply \frac{9x^{4}}{4yz} times \frac{4xy^{3}}{7z^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9x^{4}\times 4xy^{3}}{4yz\times 7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Cancel out 4y in both numerator and denominator.

$$\frac{\frac{9xy^{2}x^{4}}{7zz^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Divide \frac{9xy^{2}x^{4}}{7zz^{2}} by \frac{8yz^{2}}{x^{2}} by multiplying \frac{9xy^{2}x^{4}}{7zz^{2}} by the reciprocal of \frac{8yz^{2}}{x^{2}}.

$$\frac{9xy^{2}x^{4}x^{2}}{7zz^{2}\times 8yz^{2}}$$

Cancel out y in both numerator and denominator.

$$\frac{9xyx^{2}x^{4}}{7\times 8zz^{2}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{9x^{3}yx^{4}}{7\times 8zz^{2}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{9x^{7}y}{7\times 8zz^{2}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{9x^{7}y}{7\times 8z^{3}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{9x^{7}y}{7\times 8z^{5}}$$

Multiply 7 and 8 to get 56.

$$\frac{9x^{7}y}{56z^{5}}$$

Expand

$$\frac{9yx^{7}}{56z^{5}}$$

Short Solution Steps

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

$$\frac{\frac{3^{2}\left(x^{2}\right)^{2}}{4yz}\times \frac{4xy^{3}}{7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

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

$$\frac{\frac{3^{2}x^{4}}{4yz}\times \frac{4xy^{3}}{7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{9x^{4}}{4yz}\times \frac{4xy^{3}}{7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Multiply \frac{9x^{4}}{4yz} times \frac{4xy^{3}}{7z^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9x^{4}\times 4xy^{3}}{4yz\times 7z^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Cancel out 4y in both numerator and denominator.

$$\frac{\frac{9xy^{2}x^{4}}{7zz^{2}}}{\frac{8yz^{2}}{x^{2}}}$$

Divide \frac{9xy^{2}x^{4}}{7zz^{2}} by \frac{8yz^{2}}{x^{2}} by multiplying \frac{9xy^{2}x^{4}}{7zz^{2}} by the reciprocal of \frac{8yz^{2}}{x^{2}}.

$$\frac{9xy^{2}x^{4}x^{2}}{7zz^{2}\times 8yz^{2}}$$

Cancel out y in both numerator and denominator.

$$\frac{9xyx^{2}x^{4}}{7\times 8zz^{2}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{9x^{3}yx^{4}}{7\times 8zz^{2}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{9x^{7}y}{7\times 8zz^{2}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{9x^{7}y}{7\times 8z^{3}z^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{9x^{7}y}{7\times 8z^{5}}$$

Multiply 7 and 8 to get 56.

$$\frac{9x^{7}y}{56z^{5}}$$