Advertisements
Advertisements
Question
Evaluate:
`(27/8)^(2/3) - (1/4)^-2 + 5^0`
Advertisements
Solution
`( 27/8 )^(2/3) - (1/4)^(-2) + 5^0`
= `([ 3 xx 3 xx 3]/[ 2 xx 2 xx 2 ])^(2/3) - ([ 1 xx 1 ]/[ 2 xx 2 ])^-2 + 5^0`
= `[(3/2)^3]^(2/3) - [(1/2)^2]^-2 + 1`
= `(3/2)^( 3 xx 2/3 ) - (1/2)^[2 xx ( - 2)] + 1`
= `(3/2)^2 - (1/2)^-4 + 1`
= `3/2 xx 3/2 - 1/[(1/2)^4] + 1`
= `9/4 - 1/[ 1/2 xx 1/2 xx 1/2 xx 1/2 ] + 1`
= `9/4 - 1/[1/16] + 1`
= `9/4 - 16 + 1`
= `[ 9 - 64 + 4 ]/4`
= `(-51)/4`
APPEARS IN
RELATED QUESTIONS
Evaluate :
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`
Evaluate:
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`
Evaluate:
`(16/81 )^(-3/4) xx (49/9)^(3/2) ÷ (343/216)^(2/3)`
Simplify:
`[ 5^( n + 3 ) - 6 xx 5^( n + 1 )]/[ 9 xx 5^n - 5^n xx 2^2 ]`
Simplify :
`( 3x^2 )^(-3) xx ( x^9 )^(2/3)`
Evaluate :
`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`
Simplify the following and express with positive index :
`(3^-4/2^-8)^(1/4)`
If 1960 = 2a. 5b. 7c, calculate the value of 2-a. 7b. 5-c.
Show that :
`( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1`
Evaluate the following: `(2^3)^2`
