Advertisements
Advertisements
Question
Find the value of the following:
\[\left\{ \left( \frac{1}{3} \right)^{- 1} - \left( \frac{1}{4} \right)^{- 1} \right\}^{- 1}\]
Sum
Advertisements
Solution
We know from the property of powers that for every natural number a, a−1 = 1/a. Then:
`((1/3)^(-1)-(1/4)^(-1))^(-1)=(3-4)^(-1)` `->(a^(-1)=1/a)`
`=(-1)^(-1)`
= -1 → (a−1 = 1/a)
shaalaa.com
Is there an error in this question or solution?
RELATED QUESTIONS
Find the value of the following:
(3−1 + 4−1 + 5−1)0
Simplify:
\[\left( 3^2 - 2^2 \right) \times \left( \frac{2}{3} \right)^{- 3}\]
Simplify:
\[\left( 2^{- 1} + 3^{- 1} \right)^{- 1}\]
Express the following rational numbers with a positive exponent:
\[\left\{ \left( \frac{4}{3} \right)^{- 3} \right\}^{- 4}\]
Find x, if
\[\left( \frac{3}{2} \right)^{- 3} \times \left( \frac{3}{2} \right)^5 = \left( \frac{3}{2} \right)^{2x + 1}\]
Find x, if
\[\left( \frac{2}{5} \right)^{- 3} \times \left( \frac{2}{5} \right)^{15} = \left( \frac{2}{5} \right)^{2 + 3x}\]
Find x, if
\[\left( \frac{5}{4} \right)^{- x} \div \left( \frac{5}{4} \right)^{- 4} = \left( \frac{5}{4} \right)^5\]
For a non zero rational number a, (a3)−2 is equal to
Evaluate.
`(8^(-1)xx5^(3))/2^(-4)`
Expand the following numbers using exponents.
1256.249
