1)
Simplify the following:
((1/a)^(-4))^2
Multiply exponents. (1/a)^(-4) = a^4:
a^4^2
Multiply exponents. (a^4)^2 = a^(4×2):
a^(4×2)
4×2 = 8:
Answer: |a^8
2)
u (28 t - 7 u) + 2 t
3)
This is how I read it:
Simplify the following:
a^2/3 - a^2/12 + a/4
Put each term in a^2/3 - a^2/12 + a/4 over the common denominator 12: a^2/3 - a^2/12 + a/4 = (4 a^2)/12 - a^2/12 + (3 a)/12:
(4 a^2)/12 - a^2/12 + (3 a)/12
(4 a^2)/12 - a^2/12 + (3 a)/12 = (4 a^2 - a^2 + 3 a)/12:
(4 a^2 - a^2 + 3 a)/12
Grouping like terms, 4 a^2 - a^2 + 3 a = (4 a^2 - a^2) + 3 a:
((4 a^2 - a^2) + 3 a)/12
4 a^2 - a^2 = 3 a^2:
(3 a^2 + 3 a)/12
Factor 3 a out of 3 a^2 + 3 a:
3 a (a + 1)/12
3/12 = 3/(3×4) = 1/4:
Answer: |(a (a + 1))/4
4)
log6(12) + 1/2log6(9)
Log(12)/Log(6) + 1/2 [Log(9)/Log(6)
1.3868...... + 1/2 x 1.22629.....
=2
5)
Simplify the following:
9 y^2 + (4 y)/3 - 12 y - 2
Put each term in 9 y^2 + (4 y)/3 - 12 y - 2 over the common denominator 3: 9 y^2 + (4 y)/3 - 12 y - 2 = (27 y^2)/3 + (4 y)/3 - (36 y)/3 - 6/3:
(27 y^2)/3 + (4 y)/3 - (36 y)/3 - 6/3
(27 y^2)/3 + (4 y)/3 - (36 y)/3 - 6/3 = (27 y^2 + 4 y - 36 y - 6)/3:
(27 y^2 + 4 y - 36 y - 6)/3
4 y - 36 y = -32 y:
Answer: |(27 y^2 + -32 y - 6)/3
