I. The expression a = b , b is called the base and c is the exponent designating the power to which the base is raised. When working with exponents, three rules must be observed.
-
A) each factor may be evaluated separately and the individual products multiplied.
EXAMPLE:
4
2
= 4 x 4 = 16
4
3
= 4 x 4 x 4 = 64
THEN: 16 x 64 = 1024
The same results may be obtained by adding the exponents.
EXAMPLE:
4
2
x 4
3
= 4(2 + 3) = 4
5
= 1024
The above may be written algebraically as:
X
a
x X
b
x X
c
= X
(a + b + c)
II. The quotient of two terms containing the same base raised to any power is equal to the base raised to the difference of the algebraic sum of exponents in the numerator and the algebraic sum of the exponents in the denominator.
EXAMPLE:
2
4
Ö 2
2
= ?
Evaluating the numerator and denominator separately, the results are as follows:
2
4
Ö 2
2
= 16 Ö 4 = 4 or 2
4
Ö 2
2
= 2
(4-2)
= 2
2
= 4
The algebraic rule:
Y
a
Y
b
= Y
a
Ð b
III. One must multiply the exponents to raise a term to a power that has a base raised to a power.
EXAMPLE:
(3
2
)
3
= 9
3
= 243, OR (3
2
)
3
3
2t3
= 3
5
= 243
Math
Activities
for
Students
Write each of the following using exponents:
1. 6 . 6 . 6 = 6
3
2. 4 . 4 . 4 . 4 = 4
4
3. P . P . P . P . P = P
5
Evaluate each expression:.
1 Y = 7
2
Y = 49
2. M = 3
5
M = 243
3. T = 4
3
T = 64
4. S = 2
4
S = 16
Evaluate each expression:
1. 3y
4
if y = 2 =
2. 4r
3
if r = 3 =
3. 2m
3
if m = 5 =
Simplify the following:
|
X
8
|
B
5
|
K
2
|
|
——
|
——
|
——
|
|
X
5
|
B
2
|
K
7
|
Simplify the following:
|
81
|
27
|
243
|
|
— = 3
|
— = 9
|
—— = 81
|
|
27
|
3
|
9
|
Gerald will be going to the hospital for a bone scan. He will arrive at the nuclear medicine department at 7:45 a.m. and be injected with l5mCi of Technetium—MDP. Scanning takes place two hours after injection is administered.
What time will Gerald’s scan begin?
9:45 a.m.
A survey showed that 3/4 of the patients of nuclear medicine receive liver and spleen scans. What part of the patients do not receive liver and spleen scans?
25%
percent
Given the formula below, compute a childs dosage for a renal scan:
|
Child wt(kg) x Adult dose
|
60kg x 15
|
|
——————————Ð
|
—————
|
= 13mCi
|
|
|
70kg
|
70kg
|
The following are problems for students. The purpose of these activities is to acquaint the student with units of measure required for computing mathematical computations with one or more operations related to nuclear medicine:
-
1. Sally mixes 260g of flour, 200g of sugar, and 245 grams of butter. How much does the whole mixture weigh? ———
-
2. Susan’s dinner consists of 150g of cooked ham, 125g of potatoes, 100g of peas and 160g of fruit salad. How much does Susan’s dinner weigh? ———
-
3. One apple weighs 100g and one orange weighs 160g. How much more than two apples do two oranges weigh? ———
-
4. A box of crackers weighs 342 grams. The crackers are packed in 3 cellophane wrappers. If each of the 3 packages has the same weight, how much does each package weigh? ———
-
5. Tammy’s popsicle weighs 74g. How much does it weigh after Tammy has eaten half of it? ———
-
6. Jeff weighs 45kg and his baby brother weighs 5kg. How much more does Jeff weigh than his brother. Change the weight in kilograms to pounds. ———
-
7. Bob can lift twice as much weight as Carl. If Carl can lift 27kg, how much can Bob lift? ———
-
8. Lisa’s bicycle weighs 3kg less than her wagon. If her bicycle weighs 8kg, how much does her wagon weigh? ———
-
9. An ocean liner weighs 31,000t. It takes on 78t of cargo, 65t of passengers and luggage, 43t of food and water. What is the total weight? ———
-
10. Cindy, Jimmy and Julie weigh 108kg all together. If Cindy weighs 23kg, Jimmy weighs 38kg, how much does Julie weigh? ———
