Advertisements
Advertisements
Question
If \[x = \left( \frac{4}{5} \right)^{- 2} \div \left( \frac{1}{4} \right)^2\], find the value of x−1.
Advertisements
Solution
First, we have to find x.
\[x = \left( \frac{4}{5} \right)^{- 2} \div \left( \frac{1}{4} \right)^2\] →((a/b)n = (an)/(bn))
`=(4^(-2)/5^(-2))xx4^2`
`=4^0/5^(-2)`
`=1/56(-2)` → (a0 = 1)
Hence, the value of x−1 is:
`x^(-1)=(1/5^(-2))^(-1)`
`=(5^2)^(-1)` →(a−1 = 1/a)
`=1/5^2` →(a−1 = 1/a)
APPEARS IN
RELATED QUESTIONS
Simplify and express the result in power notation with positive exponent.
(−4)5 ÷ (−4)8
Evaluate.
`{(1/3)^(-1) - (1/4)^(-1)}^(-1)`
Write the following in exponential form:
\[\left( \frac{2}{5} \right)^{- 2} \times \left( \frac{2}{5} \right)^{- 2} \times \left( \frac{2}{5} \right)^{- 2}\]
Express the following as a rational number in the form \[\frac{p}{q}:\]
(−7)−1
Simplify:
\[\left( 4^{- 1} - 5^{- 1} \right) \div 3^{- 1}\]
Express the following rational numbers with a positive exponent:
Simplify:
By what number should (−15)−1 be divided so that the quotient may be equal to (−5)−1?
Square of \[\left( \frac{- 2}{3} \right)\] is
