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

The correct option is D 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 VII

Mathematics

Exponents in Fractions

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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Similar questions

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

Q. Find the value of each of the following:
(i)

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

(ii)

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

(iii) (2⁻¹ × 4⁻¹) ÷ 2⁻²
(iv) (5⁻¹ × 2⁻¹) ÷ 6⁻¹

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}

Q. Find the value of the given expression:

\frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \frac{1}{\sqrt{13} - \sqrt{12}} + \frac{1}{\sqrt{12} - \sqrt{11}} - \frac{1}{\sqrt{11} - \sqrt{10}} + \frac{1}{\sqrt{10} - 3}

Let $y = \frac{1}{2 + \frac{1}{3 + \frac{1}{2 + \frac{1}{3 + . . . . .}}}}$ What is the value of y?

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