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
Evaluate:
`( 27/125 )^(2/3) xx ( 9/25 )^(-3/2)`
Simplify:
`[ 5^( n + 3 ) - 6 xx 5^( n + 1 )]/[ 9 xx 5^n - 5^n xx 2^2 ]`
Simplify the following and express with positive index :
`(3^-4/2^-8)^(1/4)`
Simplify the following and express with positive index:
`[ 1 - { 1 - ( 1 - n )^-1}^-1]^-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 )`
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 )`
If a = xm + n. yl ; b = xn + l. ym and c = xl + m. yn,
Prove that : am - n. bn - l. cl - m = 1
Find the value of (23)2.
Find the value of 46 × 4−4.
`[(3/7)^-3]^4` = ______
