How do you simplify $243^{\frac{5}{2}}$ $243^{\frac{5}{2}}$ ?

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Answer 1 · 2016-10-21T23:49:56

$920, 482.81$ $920,482.81$

Using Logarithmic approach:
$243^{\frac{5}{2}}$ $243^(5/2)$
$243^{2.5}$ $243^2.5$

$log 243 = 2.3856063$ $Log 243 = 2.3856063$

$2.5 \cdot log 243 = 2.5 \cdot 2.3856063 = 5.9640157$ $2.5 * Log 243 = 2.5 * 2.3856063 = 5.9640157$

antilog $5.9640157 = 920, 482.81$ $5.9640157 = 920,482.81$

Answer 2 · 2016-10-22T12:22:14

If the question was meant to be be $243^{\frac{2}{5}}$ $243^(2/5)$

Answer is $9$ $9$

I suspect that there is a problem with the question itself and a typo has crept in.

$243 = 3^{5}$ $243 = 3^5$ .

$243$ $243$ therefore has an exact 5th root, but not an exact square root which is being asked.

Consider if the question was meant to be be $243^{\frac{2}{5}}$ $243^(2/5)$

This now means: ${(\sqrt[5]{243})}^{2}$ $(color(red)(root5 243))^2$

= $3^{2}$ $color(red)(3)^2$

= $9$ $9$

How do you simplify 24352243^{\frac{5}{2}}?