Solve 3x^2y^3/4z^2=a/12xz^3

$$\frac { 3 x ^ { 2 } y ^ { 3 } } { 4 z ^ { 2 } } = \frac { a } { 12 x z ^ { 3 } }$$

Solve for a

$$a=9z\left(xy\right)^{3}$$

$$z\neq 0\text{ and }x\neq 0$$

Solution Steps

Multiply both sides of the equation by 12xz^{3}, the least common multiple of 4z^{2},12xz^{3}.

$$3xz\times 3x^{2}y^{3}=a$$

Multiply 3 and 3 to get 9.

$$9xzx^{2}y^{3}=a$$

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

$$9x^{3}zy^{3}=a$$

Swap sides so that all variable terms are on the left hand side.

$$a=9x^{3}zy^{3}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt[3]{\frac{3a}{z}}}{3y}\text{, }&a\neq 0\text{ and }z\neq 0\text{ and }y\neq 0\\x\neq 0\text{, }&a=0\text{ and }y=0\text{ and }z\neq 0\end{matrix}\right.$$