Find the value of 1-15-2-1-13-2-1-12-2-

The correct option is B 538 Given, (1/15)^ 2 + (1/13)^ 2 + (1/12)^ 2 =(15^ 1)^ 2 +(13^ 1)^ 2+ (12^ 1)^ 2 (∵ a^ m = 1/a^m) = (15)^( 1 × 2) +(13)^( 1 × 2)+ ...

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Standard IX

Mathematics

Powers with Positive and Negative Exponents

Find the valu...

Question

Find the value of $(\frac{1}{15})^{- 2}$ + $(\frac{1}{13})^{- 2}$ + $(\frac{1}{12})^{- 2}$ .

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538

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0.226

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269

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Solution

The correct option is B
538

Given, $(\frac{1}{15})^{- 2}$ + $(\frac{1}{13})^{- 2}$ + $(\frac{1}{12})^{- 2}$

= $(15^{- 1})^{- 2}$ + $(13^{- 1})^{- 2}$ + $(12^{- 1})^{- 2}$ ( $∵ a^{- m} = \frac{1}{a^{m}}$ )

= $(15)^{(- 1 \times - 2)}$ + $(13)^{(- 1 \times - 2)}$ + $(12)^{(- 1 \times - 2)}$ ( $∵ (a^{n})^{m} = (a)^{m \times n}$ )
= $15^{2}$ + $13^{2}$ + $12^{2}$
=225 + 169 + 144

= 538

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Find the value of (115)−2 + (113)−2 + (112)−2.

The correct option is B 538 Given, (115)−2 + (113)−2 + (112)−2 =(15−1)−2 +(13−1)−2+ (12−1)−2 (∵a−m = 1am) = (15)(−1 × −2) +(13)(−1 × −2)+ (12)(−1 × −2) (∵(an)m = (a)m×n) = 152 + 132 +122 =225 + 169 + 144 = 538

Find the value of $(\frac{1}{15})^{- 2}$ + $(\frac{1}{13})^{- 2}$ + $(\frac{1}{12})^{- 2}$ .