Simplify: 5√(32)raised to power -3?

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Answer 1 · 2018-06-08T17:04:50

$\frac{1}{16000 \cdot \sqrt{2}}$ $1/(16000*sqrt(2)$

W"riting your term as

$\frac{1}{5^{3} \cdot 4^{3} \cdot 2 \cdot \sqrt{2}}$ $1/(5^3*4^3*2*sqrt(2))$

This is

$\frac{1}{16000 \cdot \sqrt{2}}$ $1/(16000*sqrt(2))$

Answer 2 · 2018-06-08T17:09:52

$\frac{1}{16000 \sqrt{2}}$ $1/(16000sqrt(2))$

$\Rightarrow {(5 \sqrt{32})}^{- 3}$ $=> (5sqrt(32))^-3$

$=> 1/(5sqrt(32))^3 color(white)(...)[∵ a^-b = 1/a^b]$

$=> 1/(5^3 × sqrt(32)^3)$

$=> 1/(125 × sqrt(32) × sqrt(32) × sqrt(32))$

$=> 1/(125 × 32sqrt(32)) color(white)(...)[∵ sqrt(a) × sqrt(a) = a]$

$=> 1/(4000sqrt(32))$

$=> 1/(4000sqrt(4 × 4 × 2))$

$=> 1/(4000 × 4 × sqrt(2))$

$=> 1/(16000sqrt(2))$