Solve for x 1/(2ab)=x/(24a^3b^2)

$\frac{1}{2 a b} = \frac{x}{24 a^{3} b^{2}}$

Rewrite the equation as $\frac{x}{24 a^{3} b^{2}} = \frac{1}{2 a b}$ .

$\frac{x}{24 a^{3} b^{2}} = \frac{1}{2 a b}$

Multiply both sides by $24 a^{3} b^{2}$ .

$\frac{x}{24 a^{3} b^{2}} (24 a^{3} b^{2}) = \frac{1}{2 a b} (24 a^{3} b^{2})$

Simplify.

Simplify the left side.

Simplify $\frac{x}{24 a^{3} b^{2}} (24 a^{3} b^{2})$ .

Rewrite using the commutative property of multiplication.

$24 \frac{x}{24 a^{3} b^{2}} (a^{3} b^{2}) = \frac{1}{2 a b} (24 a^{3} b^{2})$

Cancel the common factor of $24$ .

Factor $24$ out of $24 a^{3} b^{2}$ .

$24 \frac{x}{24 (a^{3} b^{2})} (a^{3} b^{2}) = \frac{1}{2 a b} (24 a^{3} b^{2})$

Cancel the common factor.

$24 \frac{x}{24 (a^{3} b^{2})} (a^{3} b^{2}) = \frac{1}{2 a b} (24 a^{3} b^{2})$

Rewrite the expression.

$\frac{x}{a^{3} b^{2}} (a^{3} b^{2}) = \frac{1}{2 a b} (24 a^{3} b^{2})$

Cancel the common factor of $a^{3} b^{2}$ .

Cancel the common factor.

$\frac{x}{a^{3} b^{2}} (a^{3} b^{2}) = \frac{1}{2 a b} (24 a^{3} b^{2})$

Rewrite the expression.

$x = \frac{1}{2 a b} (24 a^{3} b^{2})$

Simplify the right side.

Simplify $\frac{1}{2 a b} (24 a^{3} b^{2})$ .

Rewrite using the commutative property of multiplication.

$x = 24 \frac{1}{2 a b} (a^{3} b^{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $24$ .

$x = 2 (12) \frac{1}{2 a b} (a^{3} b^{2})$

Factor $2$ out of $2 a b$ .

$x = 2 (12) \frac{1}{2 (a b)} (a^{3} b^{2})$

Cancel the common factor.

$x = 2 \cdot 12 \frac{1}{2 (a b)} (a^{3} b^{2})$

Rewrite the expression.

$x = 12 \frac{1}{a b} (a^{3} b^{2})$

Combine $12$ and $\frac{1}{a b}$ .

$x = \frac{12}{a b} (a^{3} b^{2})$

Cancel the common factor of $a b$ .

Factor $a b$ out of $a^{3} b^{2}$ .

$x = \frac{12}{a b} (a b (a^{2} b))$

Cancel the common factor.

$x = \frac{12}{a b} (a b (a^{2} b))$

Rewrite the expression.

$x = 12 (a^{2} b)$

$x = 12 a^{2} b$