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# Reduce the following expressions

0
259
2

1: ((1/a)^-4)^2

2: (2t-7u)^2 + 28ut

3: a/4 + a^2/3 - a^2/12

4: log6(12) + 1/2log6(9)

5: 9y^2-12y+4/3y-2

Guest Feb 19, 2017
edited by Guest  Feb 19, 2017
#1
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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:

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:

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

Guest Feb 19, 2017
#2
+9490
+5

1: ((1/a)^-4)^2

2: (2t-7u)^2 + 28ut

3: a/4 + a^2/3 - a^2/12

4: log6(12) + 1/2log6(9)

5: 9y^2-12y+4/3y-2

Omi67  Feb 19, 2017