Sect 5.1 - Exponents: Multiplying And Dividing Common Bases Worksheet With Answers Page 5
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1
2
3
4
5
6
744
−28
b)
Be careful with
since they are not exponents. We will
21
6
7
5
−28x
−28
y
z
6 – 2
7 – 1
5 – 4
need to reduce that part:
=
x
y
z
2
4
21
21x
yz
4
4
6
= –
x
y
z.
3
c)
First, simplify the numerator and denominator:
2 +1
5 + 4
1 + 2
2
5
4
2
3
9
3
−6•−5a
(−6a
b
c)(−5ab
c
)
b
c
30a
b
c
=
=
1 +1
2
1+ 2
2
3
−10a
−10a
(−10ab)(ab
)
b
b
Now, perform the division:
3
9
3
30
30a
b
c
3 – 2
9 – 3
3
6
3
=
a
b
c
= – 3ab
c
.
−10
2
3
−10a
b
Concept #5
Applications of Exponents
Recall that when we calculated simple interest, we used the formula i = prt
where i was the interest, p was the principal, r was the annual interest rate
written as a decimal or fraction, and t was the time in years. This formula
depends on the principal being fixed during the lifetime of the loan which is
not always the case. Let us consider an example where interest is
calculated on the amount in the account every year.
Solve the following:
Ex. 10
Juan invests $1000 in an account paying 7% annual interest
every year on the amount in the account. How much money does he have
in the account after three years?
Solution:
For the first year, p = $1000, r = 7% = 0.07, and t = 1 year. Thus,
the interest is:
i = prt = (1000)(0.07)(1) = $70.
The total in the account is
A = p + i = 1000 + 70 = $1070
For the second year, p = $1070, r = 7% = 0.07, and t = 1 year.
Thus, the interest is:
i = prt = (1070)(0.07)(1) = $74.90.
The total in the account is
A = p + i = 1070 + 74.90 = $1144.90
For the third year, p = $1144.90, r = 7% = 0.07, and t = 1 year. Thus,
the interest is:
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