Now, ̧
¹
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aa
aa
aa
aa
1 1
3
1 1 3
33=^23 ]
1
2 3 323 [3
aa= 2 3 3 2 3
3 3
u= 8 3 3 6 3
= 24 3 6 3
= 18 3 (proved)
Activity : 1. If x 2 , what is the value of 27 x^3 54 x^2 36 x 8?- If ab 5 and ab 6 , find the value of a^3 b^3 4 (ab)^2.
- If x 5 3 , find the value of^33
1
x
x .Exercise 3⋅ 2- Find the cube with the help of the formulae :
(a) 2 x 5 (b) 2 x^2 3 y^2 (c) 4 a 5 x^2 (d) 7 m^2 2 n (e) 403 (f) 998
(g) 2 ab 3 c (h) 2 x 3 yz
- Simplify :
(a) ( 4 a 3 b)^3 3 ( 4 a 3 b)^2 ( 2 a 3 b) 3 ( 4 a 3 b)( 2 a 3 b)^2 ( 2 a 3 b)^3
(b) ( 2 xy)^3 3 ( 2 xy)^2 ( 2 xy) 3 ( 2 xy)( 2 xy)^2 ( 2 xy)^3
(c) ( 7 x 3 b)^3 ( 5 x 3 b)^3 6 x( 7 x 3 b)( 5 x 3 b)
(d) (x 15 )^3 ( 16 x)^3 3 (x 15 )( 16 x)
(e) (abc)^3 (abc)^3 6 (bc){a^2 (bc)^2 }
(f) (mn)^6 (mn)^6 12 mn(m^2 n^2 )^2
(g) (xy)(x^2 xyy^2 )(yz)(y^2 yzz^2 )(zx)(z^2 zxx^2 )
(h) ( 2 x 3 y 4 z)^3 ( 2 x 3 y 4 z)^3 12 x{ 4 x^2 ( 3 y 4 z)^2 }
- If ab 5 and ab 36 , what is the value of a^3 b^3?
- If a^3 b^3 513 and ab 3 , what is the value of ab?
- If x 19 and y 12 , find the value of 8 x^3 36 x^2 y 54 xy^2 27 y^3.
- If a 15 , what is the value of 8 a^3 60 a^2 150 a 130?
- If a 7 and b 5 , what is the value of