Evaluate-14-3-13-3-16-3

[(14)^ 3 (13)^ 3]÷(16)^ 3 =[(4)^3 (3)^3] ÷(6 )^3[∵ a^ m=1a^m] =[(4×4×4) (3×3×3)]÷(6×6×6) =[64 27]÷216 =37÷216=37×1216=37216 Hence, the value of given expression ...

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Standard IX

Mathematics

Property 1

Evaluate:[14-...

Question

Evaluate:
$[{(\frac{1}{4})}^{- 3} - {(\frac{1}{3})}^{- 3}] \div {(\frac{1}{6})}^{- 3}$

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Solution

$[{(\frac{1}{4})}^{- 3} - {(\frac{1}{3})}^{- 3}] \div {(\frac{1}{6})}^{- 3} = [(4)^{3} - (3)^{3}] \div {(6)}^{3} [∵ a^{- m} = \frac{1}{a^{m}}] = [(4 \times 4 \times 4) - (3 \times 3 \times 3)] \div (6 \times 6 \times 6) = [64 - 27] \div 216 = 37 \div 216 = 37 \times \frac{1}{216} = \frac{37}{216} Hence, the value of given expression is \frac{37}{216}$ .

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Property 1

Standard IX Mathematics

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Evaluate: [(14)−3−(13)−3]÷(16)−3

[(14)−3−(13)−3]÷(16)−3=[(4)3−(3)3]÷(6)3[∵a−m=1am]=[(4×4×4)−(3×3×3)]÷(6×6×6)=[64−27]÷216=37÷216=37×1216=37216Hence, the value of given expression is 37216.

Evaluate:
$[{(\frac{1}{4})}^{- 3} - {(\frac{1}{3})}^{- 3}] \div {(\frac{1}{6})}^{- 3}$