Advertisements
Advertisements
Question
Simplify:
`(256)^(-(4^((-3)/2))`
Advertisements
Solution
`(256)^(-(4^(-3/2))) = (256)^(-(4)^(-3/2)`
= `(256)^(-(2^2)^(-3/2))`
= `(256)^(-(2^(2 xx -3/2))` ...`[∵ b^((a^m)^n) = b^(a^(mn))]`
= `(256)^(-(2^-3))`
= `(2^8)^(-(1/2^3)`
= `(2^8)^(-1/8)`
= `2^(8 xx -1/8)`
= `2^-1`
= `1/2`
APPEARS IN
RELATED QUESTIONS
Classify the following numbers as rational or irrational:
`2-sqrt5`
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
if `x= 3 + sqrt8`, find the value of `x^2 + 1/x^2`
The rationalisation factor of \[\sqrt{3}\] is
Classify the following number as rational or irrational:
2π
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(2))`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
