Question 98iSimplify-1-4 -2 - 1-2 -2- 1-3 -2

Using law of exponents, a^ m =1/a^m ∴(1/4 )^ 2 + ( 1/2 )^ 2+ (1/3 )^ 2= (4)^2+(2)^2 +(3)^2 =16+4+9 = 29 ...

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Standard VIII

Mathematics

Power of a Power

Question 98iS...

Question

Question 98(i)

Simplify:
${(\frac{1}{4})}^{- 2} + {(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2}$

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Solution

Using law of exponents, $a^{- m} = \frac{1}{a^{m}} ∴ {(\frac{1}{4})}^{- 2} + {(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} = (4)^{2} + (2)^{2} + (3)^{2} = 16 + 4 + 9 = 29$

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Similar questions

Simplify:

${(\frac{1}{4})}^{- 2} + {(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2}$

Question 3(iii)
Find the value of:

${(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2}$

Question 3(iii)
Find the value of:

${(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2}$

Question 1(i) :

Solve:

$\frac{2}{3} + \frac{3}{4} + \frac{1}{2}$

Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [- \frac{1}{4} \times \frac{2}{3}] + [- \frac{1}{4} \times (\frac{- 4}{7})]$
(b) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [\frac{1}{4} \times \frac{2}{3}] - (\frac{- 4}{7})$
(c) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = \frac{2}{3} + (- \frac{1}{4}) \times \frac{- 4}{7}$
(d) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = {\frac{2}{3} + (\frac{- 4}{7})} - \frac{1}{4}$

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Power of a Power

Standard VIII Mathematics

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Question 98(i) Simplify: (14)−2+(12)−2+(13)−2

Using law of exponents, a−m=1am∴(14)−2+(12)−2+(13)−2=(4)2+(2)2+(3)2=16+4+9=29

Question 98(i)

Simplify:
${(\frac{1}{4})}^{- 2} + {(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2}$

Using law of exponents, $a^{- m} = \frac{1}{a^{m}} ∴ {(\frac{1}{4})}^{- 2} + {(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} = (4)^{2} + (2)^{2} + (3)^{2} = 16 + 4 + 9 = 29$