Advertisements
Advertisements
Question
Find the value of (2−1 × 4−1) ÷2−2.
Sum
Advertisements
Solution
`(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`
shaalaa.com
Is there an error in this question or solution?
Chapter 10: Exponents and Powers - EXERCISE 10.1 [Page 125]
APPEARS IN
RELATED QUESTIONS
Evaluate.
`{(1/3)^(-1) - (1/4)^(-1)}^(-1)`
Evaluate:
\[\left( \frac{- 1}{2} \right)^{- 1}\]
Express the following as a rational number in the form \[\frac{p}{q}:\]
\[\left( \frac{1}{4} \right)^{- 1}\]
Express the following as a rational number in the form \[\frac{p}{q}:\]
\[\left( \frac{3}{5} \right)^{- 1} \times \left( \frac{5}{2} \right)^{- 1}\]
Express the following rational numbers with a negative exponent:
\[\left\{ \left( \frac{3}{2} \right)^4 \right\}^{- 3}\]
Simplify:
\[\left( 3^2 - 2^2 \right) \times \left( \frac{2}{3} \right)^{- 3}\]
\[\left( \frac{2}{3} \right)^{- 5}\] is equal to
\[\left( \frac{- 1}{2} \right)^5 \times \left( \frac{- 1}{2} \right)^3\] is equal to
\[\left( \frac{- 1}{5} \right)^3 \div \left( \frac{- 1}{5} \right)^8\] is equal to
The multiplicative inverse of `(3/2)^2` is not equal to `(2/3)^-2`.
