Math 151 - ICA #3 Summer 2016 Section 8349
Instructor: John Kwon
In-Class Assignment #3: Negative Exponents and Scientific Notation - Solution
1. Simplify the expression below:
9a−1 b4 c−2
18a3 bc−4
−3
Answer. The simplest way to do this is to: (1) first simplify the expression inside the parenthesis,
and then (2) take the reciprocal of the resulting expression while taking off the negative sign in
the outside exponent. To simplify the expression inside the parenthesis, we will first push any
factor with negative exponents through to the other side of the fraction and change the exponents
to positive. Doing this yields
−1 4 −2 −3
−3
9a b c
9b4 c4
=
.
18a3 bc−4
18a3 a1 bc2
Now simplify the coefficients and each of the variables:
−3
3 2 −3
b c
9b4 c4
=
3
1
2
18a a bc
2a4
then, finally, take the reciprocal of the resulting fraction inside the parenthesis to take off the
negative sign in the outside exponent and simplify:
b3 c2
2a4
−3
=
2a4
b3 c2
3
=
23 a12
=
b9 c6
8a12
.
b9 c6
This is the entire work that should be shown:
3 2 −3
4 3
−3
−1 4 −2 −3
9b4 c4
b c
2a
23 a12
9a b c
=
=
=
=
=
18a3 bc−4
18a3 a1 bc2
2a4
b3 c2
b9 c6
8a12
.
b9 c6
2. Perform the operation below and express the answer in scientific notation .
5.7 × 102
7.6 × 10−5
Answer. Dividing 5.7 by 7.6 yields
5.7
= 0.75 .
7.6
The powers of 10 can be simplified as
102
= 102−(−5) = 102+5 = 107 .
10−5
So the entire work to be shown is:
5.7 × 102
5.7
102
=
×
= 0.75 × 107 = 7.5 × 106 .
7.6 × 10−5
7.6 10−5