Solve for m
m=-\frac{1}{160}=-0.00625
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\frac{m}{-\frac{1}{8}}\sqrt{\frac{25}{4}}\sqrt{\left(\frac{8}{3}\right)^{2}}=3^{-1}
Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.
\frac{m}{-\frac{1}{8}}\times \frac{5}{2}\sqrt{\left(\frac{8}{3}\right)^{2}}=3^{-1}
Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.
\frac{m}{-\frac{1}{8}}\times \frac{5}{2}\sqrt{\frac{64}{9}}=3^{-1}
Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.
\frac{m}{-\frac{1}{8}}\times \frac{5}{2}\times \frac{8}{3}=3^{-1}
Rewrite the square root of the division \frac{64}{9} as the division of square roots \frac{\sqrt{64}}{\sqrt{9}}. Take the square root of both numerator and denominator.
\frac{m}{-\frac{1}{8}}\times \frac{20}{3}=3^{-1}
Multiply \frac{5}{2} and \frac{8}{3} to get \frac{20}{3}.
\frac{m}{-\frac{1}{8}}\times \frac{20}{3}=\frac{1}{3}
Calculate 3 to the power of -1 and get \frac{1}{3}.
\frac{m}{-\frac{1}{8}}=\frac{1}{3}\times \frac{3}{20}
Multiply both sides by \frac{3}{20}, the reciprocal of \frac{20}{3}.
\frac{m}{-\frac{1}{8}}=\frac{1}{20}
Multiply \frac{1}{3} and \frac{3}{20} to get \frac{1}{20}.
m=\frac{1}{20}\left(-\frac{1}{8}\right)
Multiply both sides by -\frac{1}{8}.
m=-\frac{1}{160}
Multiply \frac{1}{20} and -\frac{1}{8} to get -\frac{1}{160}.
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