Advertisements
Advertisements
Question
Evaluate the following:
`(2^3 xx 3^5 xx 24^2)/(12^2 xx 18^3 xx 27)`
Advertisements
Solution
`(2^3 xx 3^5 xx 24^2)/(12^2 xx 18^3 xx 27)`
= `(2^3 xx 3^5 xx (2^3 xx 3)^2)/((2^2 xx 3^2)^2 xx (2 xx 3^2)^3 xx (3^3))`
= `(2^3 xx 3^5 xx 2^6 xx 3^2)/(2^4 xx 3^2 xx 2^3 xx 3^6 xx 3^3)`
= `(2^9 xx 3^7)/(2^7 xx 3^11)`
= `(2^(9 - 7))/(3^(11 - 7))`
= `(2^2)/(3^4)`
= `(4)/(81)`.
APPEARS IN
RELATED QUESTIONS
Solve for x : 22x+1 = 8
Solve : `[3^x]^2` : 3x = 9 : 1
If ax = by = cz and b2 = ac, prove that: y = `[2xz]/[x + z]`
Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
Evaluate the following:
`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`
Evaluate the following:
`9^(5/2) - 3 xx 5^0 - (1/81)^((-1)/2)`
Solve for x:
9 x 81x = `(1)/(27^(x - 3)`
Solve for x:
`sqrt((8^0 + 2/3)` = (0.6)2-3x
Find the value of k in each of the following:
`(root(3)(8))^((-1)/(2)` = 2k
If `x^(1/3) + y^(1/3) + z^(1/3) = 0`, prove that (x + y + z)3 = 27xyz
