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How do you solve $125 x^{- \frac{3}{4}} = 64$ $125x^(-3/4)=64$ ?

1 Answer

Jun 2, 2015

If $125 x^{- \frac{3}{4}} = 64$ $125 x^(-3/4) = 64$

$XXXXX$ $color(white)("XXXXX")$ ${(5 x^{- \frac{1}{4}})}^{3} = 4^{3}$ $(5x^(-1/4))^3 = 4^3$

$XXXXX$ $color(white)("XXXXX")$ $5 x^{- \frac{1}{4}} = 4$ $5x^(-1/4) = 4$

$XXXXX$ $color(white)("XXXXX")$ $x^{- \frac{1}{4}} = \frac{4}{5}$ $x^(-1/4) = 4/5$

$XXXXX$ $color(white)("XXXXX")$ $\frac{1}{x^{\frac{1}{4}}} = \frac{4}{5}$ $1/(x^(1/4)) = 4/5$

$XXXXX$ $color(white)("XXXXX")$ $\frac{1}{x} = {(\frac{4}{5})}^{4} = \frac{256}{625}$ $1/x = (4/5)^4 = 256/625$

$XXXXX$ $color(white)("XXXXX")$ $x = \frac{625}{256} = 2.441406$ $x = 625/256 = 2.441406$

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