Advertisements
Advertisements
Question
Simplify the following and express with positive index :
`(32)^(-2/5) ÷ (125)^(-2/3)`
Advertisements
Solution
`(32)^(-2/5) ÷ (125)^(-2/3)`
= `[(32)^(-2/5)/(125)^(-2/3)]`
= `(125)^(2/3)/(32)^(2/5)`
= `( 5 xx 5 xx 5 )^(2/3)/( 2 xx 2 xx 2 xx 2 xx 2 )^(2/5)`
= `(5^3)^(2/3)/(2^5)^(2/5)`
= `5^2/2^2`
= `25/4`
= `(5/2)^2`
APPEARS IN
RELATED QUESTIONS
Simplify :
`( 8x^3 ÷ 125y^3 )^(2/3)`
Simplify :
`( a + b )^(-1) . ( a^(-1) + b^(-1) )`
Simplify:
`[ 5^( n + 3 ) - 6 xx 5^( n + 1 )]/[ 9 xx 5^n - 5^n xx 2^2 ]`
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.
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 )`
Find the value of (23)2.
