Units 1 and 12 Review

1A Laws of Exponents

100

Describe the Quotient Rule

a^m/aⁿ=a^m-n

200

Describe the difference between the Product Rule and the Power of a Power Rule

Product Rule- Add exponents 

ex) a^m × aⁿ = a^(m+n)

Power of a Power Rule- Multiply exponents 

• (a^m)ⁿ = a^mn

300

Simplify (2x²y)³/8xy

x⁵y²

1.A #45, Green

400

Solve 25^2x+4 = 125x5^x-1

x=-2

1.A #53, Blue

500

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

1B Operations in the form of a​^x

100

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 10^k

200

Write in Standard Index Form

0.02219

2.219 x 10^-2

300

Write in Standard Index Form 

(5.7x10¹³) + (4.3x10¹²)

6.13x10¹³

1.B #13b, Non-colored

400

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.

500

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

1C Logarithms

100

Convert exponent form to log form

a=b^x --> log_ba=x

200

Describe change of base log formula 

log_ab= log_cb/log_ca

300

Solve and find exact solution 

10^x-2=70

2+log7

1.C #32a, Non-colored

400

Simplify 

ln(e^ae^b)

a+b 

1.C #39, Green

500

Evaluate log10x-logx where x is a positive number

1 

1.C #51, Black 

12A Laws of Exponents with Rational Exponents

100

a^1/n = ?

a^1/n = ⁿ√a

200

Evaluate 36^3/2

36^3/2 = 216

300

Evaluate 64^-2/3

64^-2/3 = 1/16

400

Write 17x²/⁴√x in the form kxⁿ

17x²/⁴√x = 17x^7/4

500

Solve 

log2(x+3)=3

5