Solve for z A=3/4xy^2z

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

Step 1

Rewrite the equation as $\frac{3}{4} \cdot (x y^{2} z) = A$ .

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

Step 2

Multiply both sides of the equation by $\frac{4}{3}$ .

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

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

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

Combine $x$ and $\frac{3}{4}$ .

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

Combine $y^{2}$ and $\frac{x \cdot 3}{4}$ .

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

Combine $\frac{y^{2} (x \cdot 3)}{4}$ and $z$ .

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

Combine.

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y^{2} (x) z$ by $1$ .

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

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

Simplify the right side.

Combine $\frac{4}{3}$ and $A$ .

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

Step 4

Divide each term in $y^{2} x z = \frac{4 A}{3}$ by $y^{2} x$ and simplify.

Divide each term in $y^{2} x z = \frac{4 A}{3}$ by $y^{2} x$ .

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

Simplify the left side.

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $z$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$z = \frac{4 A}{3} \cdot \frac{1}{y^{2} x}$

Combine.

$z = \frac{4 A \cdot 1}{3 (y^{2} x)}$

Multiply $4$ by $1$ .

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

Solve for z A=3/4xy^2z

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