How do you simplify $t^{- \frac{5}{4}}$ $t^ (-5 /4)$ ?

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Answer 1 · 2018-05-04T05:36:34

$\frac{1}{\sqrt[4]{t^{5}}}$ $1/(root4(t^5)$

Expression $= t^{- \frac{5}{4}}$ $= t^(-5/4)$

Here we will use the following properties of exponents:

(i) $t^{- n} = \frac{1}{t^{n}}$ $t^-n = 1/t^n$

(ii) $t^{\frac{m}{n}} = {(t^{m})}^{\frac{1}{n}}$ $t^(m/n) = (t^m)^(1/n)$

(iii) $t^{\frac{1}{n}} = \sqrt[n]{t}$ $t^(1/n) = rootn(t)$

Apply (i)
Expression $= \frac{1}{t^{\frac{5}{4}}}$ $= 1/t^(5/4)$

Apply (ii)
Expression $= \frac{1}{{(t^{5})}^{\frac{1}{4}}}$ $= 1/(t^5)^(1/4)$

Apply (iii)
Expression $= \frac{1}{\sqrt[4]{t^{5}}}$ $= 1/(root4(t^5)$

How do you simplify t−54t^ (-5 /4)?