PSSA 1.2 Powers, Roots, Exponents, and Scientific Notation
Powers
See rules for Exponents in your text on page 3. Use the rules to simplify the following.
3 2 ⋅ 35
6 2 ⋅ 63
64
23 ⋅ 27
2 2 ⋅ 43
5 2 ⋅ 55
5 0 ⋅ 58
(2 2 ) 3
(3)−2
(5 )
(4)−3
(3 )
(2 )
2 4
− 2 −3
3 5
See Model Problems on page 3 for more practice.
Roots
When solving the equation
x 2 = 25
take the 2nd root of both sides of the equation.
When solving the equation
x 3 = 64
take the 3rd root of both sides of the equation.
When solving the equation
x 4 = 16
take the 4th root of both sides of the equation.
You can use your graphing calculator to determine roots. To find the 4th root of 16, for example,
4
On the home screen, enter the number 4
16
MATH
5: x
ENTER
16
ENTER
Scientific Notation
A number in scientific notation is expressed as a product of two factors.
(a number between 1 and 10) X (a power of 10)
4,300 = 4.3 x 103
0.00127 = 1.27 x 10-3
12,756.081 = 1.2756081 x 104
To write a number in scientific notation, move the decimal until you have only 1 digit to the left of the decimal.
When you move the decimal to the left, you must multiply by a positive power of 10.
When you move the decimal to the right, you must multiply by a negative power of 10.
Rewrite the following in scientific notation.
10,257
485
817.91
5.875
0.000128
0.058192
7/8
1/10
89/100
To multiply numbers in scientific notation, multiply the decimal numbers together and then add the exponents
on the powers of ten.
(4.301 x 105)(7.8 x 103)
(1.2 x 1012)(2.5 x 1012)
Homework: p. 5 (1-12) + Worksheet
(2.1 x 102)(7.32 x 103)