Advertisements
Advertisements
Question
Simplify the following and express with positive index:
`[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1`
Solution
`[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1`
= `[1 - { 1 - 1/( 1 - n ) }^-1]^-1`
= `[1 - { (1-n-1)/( 1 - n ) }^-1]^-1`
= `[1 - { (-n)/( 1 - n ) }^-1]^-1`
= `[1 - { (1-n)/(- n ) }]^-1`
= `[ (-n- 1 + n )/-n ]^-1`
= `[(-1)/-n]^-1`
= n
APPEARS IN
RELATED QUESTIONS
Evaluate :
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`
Evaluate:
`( 27/125 )^(2/3) xx ( 9/25 )^(-3/2)`
Evaluate :
`7^0 xx (25)^(-3/2) - 5^(-3)`
Evaluate:
`(27/8)^(2/3) - (1/4)^-2 + 5^0`
Simplify :
`[ 8^3a xx 2^5 xx 2^(2a) ]/[ 4 xx 2^(11a) xx 2^(-2a) ]`
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 )`
If a = xm + n. yl ; b = xn + l. ym and c = xl + m. yn,
Prove that : am - n. bn - l. cl - m = 1
Evaluate the following: `(3^2)^2`
`[(3/7)^-3]^4` = ______
