Iii Find the value of- 1-2 -2- 1-3 -2- 1-4 -2

( 1/2 )^ 2+ ( 1/3 )^ 2+ ( 1/4 )^ 2 =(2^ 1)^ 2+(3^ 1)^ 2+(4^ 1)^ 2 [∵ a^ m=1/a^m ] =2^(2)+3^(2)+4^(2) [∵ (a^m)^n=a^m nbsp;× n ] = 2^2+3^2+4^2 =4+ ...

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Standard VIII

Mathematics

Power of a Power

iii Find the ...

Question

Question 3(iii)
Find the value of:

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

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Solution

${(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2} = (2^{- 1})^{- 2} + (3^{- 1})^{- 2} + (4^{- 1})^{- 2} [∵ a^{- m} = \frac{1}{a^{m}}] = 2^{(2)} + 3^{(2)} + 4^{(2)} [∵ (a^{m})^{n} = a^{m \times n}] = 2^{2} + 3^{2} + 4^{2} = 4 + 9 + 16 = 29$

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Similar questions

Find the value of:

$(1) (2^{0} + 3^{- 1}) \times 3^{2}$

$(i i) (2^{- 1} \times 3^{- 1}) \div 2^{- 3}$

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

Q. Find the value of:
(i) (2⁰ + 3⁻¹) × 3²
(ii) (2⁻¹ × 3⁻¹) ÷ 2⁻³
(iii)

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

Question 91

Solve the following.
$(i) 100^{- 10} (i i) 2^{- 2} \times 2^{- 3} (i i i) {(\frac{1}{2})}^{- 2} \div {(\frac{1}{2})}^{- 3}$

Find five rational numbers between

(i)

(ii)

(iii)

Simplify:

$(i) {{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}} \div {(\frac{1}{4})}^{- 3} (i i) (3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3} (i i i) {(\frac{1}{2}) \times (- 4)^{- 1}}^{- 1} (i v) {[{{(\frac{- 1}{4})}^{2}}^{- 2}]}^{- 1} (v) {{(\frac{2}{3})}^{2}}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times 6^{- 1}$

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Power of a Power

Standard VIII Mathematics

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Question 3(iii) Find the value of: (12)−2+(13)−2+(14)−2

(12)−2+(13)−2+(14)−2=(2−1)−2+(3−1)−2+(4−1)−2 [∵a−m=1am]=2(2)+3(2)+4(2) [∵(am)n=am×n]=22+32+42=4+9+16=29

Question 3(iii)
Find the value of:

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

${(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2} = (2^{- 1})^{- 2} + (3^{- 1})^{- 2} + (4^{- 1})^{- 2} [∵ a^{- m} = \frac{1}{a^{m}}] = 2^{(2)} + 3^{(2)} + 4^{(2)} [∵ (a^{m})^{n} = a^{m \times n}] = 2^{2} + 3^{2} + 4^{2} = 4 + 9 + 16 = 29$