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7-4-8. Exponents and Roots

Name _____________________________________________________   Date __________________    Score _________

Topics

  • Understanding exponents and roots.
  • Converting between exponents and decimals.
  • Simplifying exponential equations, including negative exponents.
  • Converting between scientific and decimal notation
  • Solving absolute value equations. (Remember: There are usually two solutions.)

Questions

1.
Which operation is the inverse of an exponent?
20 points
  1. Finding the sum
  2. Finding the quotient
  3. Finding the difference
  4. Finding the root
 
2.
Which number is the base in the power $5^2$?
20 points
 
3.
Which number is the exponent in the power $12^4$?
20 points
 
4.
Simplify: $4^2 =$
20 points
 
5.
Write in decimal form:
$5.4 \times 10^2 =$
20 points
 
6.
Simplify: $34^{-2} =$
20 points
 
7.
Write in exponential form:
$(-4)(-4)(-4)(-4) =$
20 points
 
8.
Convert to decimal form:
$5.6 \times 10^{-4} =$
Hint: Our normal number system is in decimal form.
20 points
 
9.
Simplify: $14^0 =$
20 points
 
10.
Write in Scientific Notation:
$45,000,000,000,000 = $
Hint: How many places do you have to move the decimal point?
20 points
 
11.
Write in Scientific Notation:
$0.0000063 = $
Hint: The number is smaller than 1.
20 points
 
12.
True or False: $\sqrt{2^2}=4$
20 points
  1. True
  2. False
 
13.
True or False: $3^3 = (3)(3)(3) = 9$
Hint: Careful! Don’t jump to conclusions.
20 points
  1. True
  2. False
 
14.
Simplify: $-3^3 =$
20 points
 
15.
Simplify: $(-3)^4 =$
20 points
 
16.
Simplify: $-3^4 =$
Hint: The exponent ONLY applies to what is directly in front of it.
20 points
 
17.
Simplify: $(-10)^{-2} =$
Hint: The exponent applies to everything in the parentheses.
20 points
 
18.
Simplify: $(10)^3 =$
20 points
 
19.
Simplify: $36^1 =$
20 points
 
20.
Simplify: $ \dfrac{15x^6}{3x^6} = $
20 points
 
21.
Simplify: $\left( \dfrac{2}{5} \right)^2 = $
20 points
 
22.
Simplify: $(30m)(\frac{1}{3}m^4) =$
Hint: Don’t let the parentheses fool you!
20 points
 
23.
Simplify: $(15x^2)(2x^4) =$
20 points
 
24.
Simplify: $\dfrac{-50x^5}{5x} =$
Hint: Fractions are division.
20 points
 
25.
Simplify: $\dfrac{4a^2b^4c^7x^5}{2a^2b^4c^7x^4} =$
Hint: Can you cross-cancel?
20 points
 
26.
Simplify: ${(2^3)}^2 = $
Hint: Since exponents are multiple multiplication, this is multiple, multiple multiplication.
20 points
 
27.
Solve for x: $|x - 4| + 2 = 6$
Hint: There are two solutions.
20 points
 
Possible Points: 540
 

Solutions

  1.    Finding the root
  2.    $5$
  3.    4
  4.    $16$
  5.    $540$
  6.    $\frac{1}{1156}$
  7.    $(-4)^4$
  8.    $0.00056$
  9.    $1$
  10.    $4.5 \times 10^{13}$
  11.    $6.3 \times 10^{-6}$
  12.    False
  13.    False
  14.    $-27$
  15.    $81$
  16.    $-81$
  17.    $-\frac{1}{100}$
  18.    $1,000$
  19.    $36$
  20.    $ 3 $
  21.    $\frac{4}{25}$
  22.    $-10m^5$
  23.    $30x^6$
  24.    $10x^4$
  25.    $2x$
  26.    $64$
  27.    $x = 0$ and $x = 8$