Solve frac{(x^{3}y^{2})^3*2xy^-4z^4}{2yzx^-2}

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

Evaluate

$$yz^{3}x^{12}$$

Solution Steps

Cancel out 2z in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{x^{3}z^{3}y^{6}\left(x^{3}\right)^{3}}{y^{5}}$$

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

$$\frac{x^{3}z^{3}y^{6}x^{9}}{y^{5}}$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{x^{12}z^{3}y^{6}}{y^{5}}$$

Cancel out y^{5} in both numerator and denominator.

$$yz^{3}x^{12}$$

Expand

$$yz^{3}x^{12}$$

Solution Steps

Cancel out 2z in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{x^{3}z^{3}y^{6}\left(x^{3}\right)^{3}}{y^{5}}$$

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

$$\frac{x^{3}z^{3}y^{6}x^{9}}{y^{5}}$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{x^{12}z^{3}y^{6}}{y^{5}}$$

Cancel out y^{5} in both numerator and denominator.

$$yz^{3}x^{12}$$