Identify equation and goal: Identify the equation and the goal of solving for m. We have the equation -(2)/(3)m = (8)/(27) and we want to find the value of m.Isolate m by multiplying: Isolate m by multiplying both sides of the equation by the reciprocal of -(2)/(3), which is -3/2. Multiplying both sides by -3/2 gives us m = (8)/(27) * (-3/2).Simplify right side: Simplify the right side of the equation by multiplying the numerators and denominators. (8 * -3) / (27 * 2) = -24 / 54.Reduce fraction: Reduce the fraction -24 / 54 by finding the greatest common divisor (GCD) of 24 and 54, which is 6. Divide both the numerator and the denominator by 6. -24 / 54 = (-24 / 6) / (54 / 6) = -4 / 9.Check solution: Check the solution by substituting m = -4 / 9 back into the original equation. -(2)/(3) * (-4 / 9) = (8)/(27). Simplify the left side: 2 * 4 / (3 * 9) = 8 / 27, which matches the right side.

Precalculus

Evaluate rational exponents

Full solution

-\frac{2}{3} m=\frac{8}{27}

Identify equation and goal: Identify the equation and the goal of solving for $m$ . We have the equation $-\frac{2}{3}m = \frac{8}{27}$ and we want to find the value of $m$ .
Isolate m by multiplying: Isolate m by multiplying both sides of the equation by the reciprocal of $-\frac{2}{3}$ , which is $-\frac{3}{2}$ . $\newline$ Multiplying both sides by $-\frac{3}{2}$ gives us $m = \frac{8}{27} \times \left(-\frac{3}{2}\right)$ .
Simplify right side: Simplify the right side of the equation by multiplying the numerators and denominators. $\newline$ $(8 \times -3) / (27 \times 2) = -24 / 54$ .
Reduce fraction: Reduce the fraction $-24 / 54$ by finding the greatest common divisor (GCD) of $24$ and $54$ , which is $6$ . Divide both the numerator and the denominator by $6$ . $-24 / 54 = (-24 / 6) / (54 / 6) = -4 / 9$ .
Check solution: Check the solution by substituting $m = -\frac{4}{9}$ back into the original equation. $-\frac{2}{3} \times \left(-\frac{4}{9}\right) = \frac{8}{27}$ . Simplify the left side: $\frac{2 \times 4}{3 \times 9} = \frac{8}{27}$ , which matches the right side.