Find- 125-1-3 - Maths Q-A

Evaluate the Expression:The given expression is,(125)^ 1/3=(5× 5× 5)^ 1/3 =(5^3)^ 1/3 =5^ 1 [∵a^ x=1/a^ ...

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Standard IX

Mathematics

Exponential Representation for Irrational Numbers

Find: 125^1/3...

Question

Find: ${(125)}^{- \frac{1}{3}}$

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Solution

Evaluate the Expression:
The given expression is,
${(125)}^{- \frac{1}{3}} = {(5 \times 5 \times 5)}^{- \frac{1}{3}}$
$= {(5^{3})}^{- \frac{1}{3}}$
$= 5^{- 1}$ $[∵ a^{- x} = \frac{1}{a^{x}}]$
$= \frac{1}{5}$
Hence, the required answer is $\frac{1}{5}$ .

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Find: 125-13

Evaluate the Expression:The given expression is,125-13=5×5×5-13 =53-13 =5-1 ∵a-x=1ax =15Hence, the required answer is 15.

Find: ${(125)}^{- \frac{1}{3}}$

Evaluate the Expression:
The given expression is,
${(125)}^{- \frac{1}{3}} = {(5 \times 5 \times 5)}^{- \frac{1}{3}}$
$= {(5^{3})}^{- \frac{1}{3}}$
$= 5^{- 1}$ $[∵ a^{- x} = \frac{1}{a^{x}}]$
$= \frac{1}{5}$
Hence, the required answer is $\frac{1}{5}$ .