Advertisements
Advertisements
प्रश्न
Evaluate:
`(27/8)^(2/3) - (1/4)^-2 + 5^0`
Advertisements
उत्तर
`( 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
संबंधित प्रश्न
Simplify :
`( 8x^3 ÷ 125y^3 )^(2/3)`
Simplify :
`( a + b )^(-1) . ( a^(-1) + b^(-1) )`
Evaluate :
`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`
Simplify the following and express with positive index :
`([27^-3]/[9^-3])^(1/5)`
If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a x 2-b x 5-c.
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`
Simplify:
`( x^a/x^b)^( a^2 + ab + b^2 ) xx (x^b/x^c)^(b^2 + bc + c^2) xx (x^c/x^a)^( c^2 + ca + a^2 )`
Find the value of 10−3.
Find the value of (23)2.
