1A Laws of Exponents
Describe the Quotient Rule
am/an=am-n
What are the two rules when converting an expression to Standard Index Form, (aka. Scientific Notation(?
1. Coefficient must be 1≤a≤10
2. Base must be 10 with k as an integer.
a x 10k
Convert exponent form to log form
a=bx --> logba=x
a1/n = ?
a1/n = n√a
Describe the difference between the Product Rule and the Power of a Power Rule
Product Rule- Add exponents
ex) am × an = a(m+n)
Power of a Power Rule- Multiply exponents
Write in Standard Index Form
0.02219
2.219 x 10-2
Describe change of base log formula
logab= logcb/logca
Evaluate 363/2
363/2 = 216
Simplify (2x2y)3/8xy
x5y2
1.A #45, Green
Write in Standard Index Form
(5.7x1013) + (4.3x1012)
6.13x1013
1.B #13b, Non-colored
Solve and find exact solution
10x-2=70
2+log7
1.C #32a, Non-colored
Evaluate 64-2/3
64-2/3 = 1/16
Solve 25^2x+4 = 125x5^x-1
x=-2
1.A #53, Blue
Compare and contrast the uses of Standard Index Form and decimal notation.
Compare: Both are representations of the same number
Contrast: Standard Index Form helps visualize the scale of the number; however, decimal notation is more direct and simpler for basic equations.
Simplify
ln(eaeb)
a+b
1.C #39, Green
Write 17x2/4√x in the form kxn
17x2/4√x = 17x7/4
Without using a calculator, which is larger out of 2^7000 and 5^3000. Justify your answer.
2^7000 is larger, because (128)^1000 is greater than (125)^1000
1.A #60, Black
The number of atoms in a balloon is approximately 6.0 × 1023. Theoretical physics predicts that there are approximately 1080 atoms in the known universe. What proportion of atoms in the known universe are found in the balloon?
6.0 x 10-57
1.B #21, Green
Evaluate log10x-logx where x is a positive number
1
1.C #51, Black
Solve
log2(x+3)=3
5