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प्रश्न
Find the value of (2−1 × 4−1) ÷2−2.
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उत्तर
`(2^(−1) × 4^(−1)) ÷ 2^(−2)`
= `[2^-1 xx (2^-2)^-1] ÷ 2^-2`
= `[2^-1 xx 2^-2]÷ 2^-2` ...[∵ (am)n = amn]
= `[2^(-1 + (-2))]÷2^-2` ...[∵ am × an = am+n]1
= `[2^(-1-2) ÷ 2^-2]`
= `2^-3 ÷ 2^-2`
= `2^(-3 - (-2))` .....[∵ am ÷ an = am−n]
= 2−3+2 = 2−1
= `1/2`
संबंधित प्रश्न
Evaluate.
3−2
Find the value of the following:
\[\left( \frac{1}{2} \right)^{- 1} + \left( \frac{1}{3} \right)^{- 1} + \left( \frac{1}{4} \right)^{- 1}\]
Simplify:
Express the following rational numbers with a positive exponent:
By what number should \[\left( \frac{1}{2} \right)^{- 1}\] be multiplied so that the product may be equal to \[\left( \frac{- 4}{7} \right)^{- 1} ?\]
Find x, if \[\left( \frac{1}{4} \right)^{- 4} \times \left( \frac{1}{4} \right)^{- 8} = \left( \frac{1}{4} \right)^{- 4x}\]
Which of the following is not equal to \[\left( \frac{- 3}{5} \right)^4 ?\]
Which of the following is not reciprocal of \[\left( \frac{2}{3} \right)^4 ?\]
Which of the following numbers is not equal to \[\frac{- 8}{27}?\]
(a) \[\left( \frac{2}{3} \right)^{- 3}\]
(b) \[- \left( \frac{2}{3} \right)^3\]
(c) \[\left( - \frac{2}{3} \right)^3\]
(d) \[\left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right)\]
Express 3–5 × 3–4 as a power of 3 with positive exponent.
