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प्रश्न
Simplify the following and express with a positive index:
`(32)^(-2/5) ÷ (125)^(-2/3)`
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उत्तर
`(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`
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संबंधित प्रश्न
Evaluate :
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`
Evaluate:
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`
Evaluate:
`7^0 xx (25)^(-3/2) - 5^(-3)`
Simplify :
`( 8x^3 ÷ 125y^3 )^(2/3)`
Evaluate:
`(27/8)^(2/3) - (1/4)^-2 + 5^0`
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.
Simplify:
`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`
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.
