Advertisements
Advertisements
Question
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
Advertisements
Solution
`(8^(1/3) xx 16^(1/3))/(32^(- 1/3)) = ((2^3)^(1/3) xx (2^4)^(1/3))/((2^5)^(-1/3))` ...[∵ (am)n = amn]
= `(2^(3 xx 1/3) xx 2^(4 xx 1/3))/(2^(5 xx -1/3))`
= `(2^(3/3 + 4/3))/(2^(-5/3))` ...`[∵ a^m/a^n = a^(m - n)]`
= `2^(7/3)/(2^(-5/3))`
= `2^(7/3 + 5/3)`
= `2^(12/3)`
= 24
= 16
APPEARS IN
RELATED QUESTIONS
Classify the following numbers as rational or irrational:
`2-sqrt5`
Rationalise the denominator of the following:
`1/sqrt7`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`3/sqrt10`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt5 + 1)/sqrt2`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
After rationalising the denominator of `7/(3sqrt(3) - 2sqrt(2))`, we get the denominator as ______.
The value of `(sqrt(32) + sqrt(48))/(sqrt(8) + sqrt(12))` is equal to ______.
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`(sqrt(10) - sqrt(5))/2`
