Podcast
Questions and Answers
What is the simplified form of $4^2 \times 4^5$?
What is the simplified form of $4^2 \times 4^5$?
- $4^7$ (correct)
- $16^3$
- $4^3$
- $8^4$
What is the result of $(-3)^2 \times (-3)^3$?
What is the result of $(-3)^2 \times (-3)^3$?
- $(-3)^6$
- $(-3)^5$ (correct)
- $(-9)^2$
- $(-3)^0$
What is the value of $3^{-2}$?
What is the value of $3^{-2}$?
- $\frac{1}{3}$
- $9$
- $3$
- $\frac{1}{9}$ (correct)
What is the coefficient when $2.5 \times 10^4$ is expressed in scientific notation?
What is the coefficient when $2.5 \times 10^4$ is expressed in scientific notation?
In scientific notation, which of the following represents $870,000$?
In scientific notation, which of the following represents $870,000$?
What does $10^3 \div 10^5$ simplify to?
What does $10^3 \div 10^5$ simplify to?
What is the standard form of $4.5 \times 10^7$?
What is the standard form of $4.5 \times 10^7$?
Which of the following represents $0.0000016$ in scientific notation?
Which of the following represents $0.0000016$ in scientific notation?
What is the result of multiplying $(5.25 imes 10^{-8})$ and $(4 imes 10^{3})$ in scientific notation?
What is the result of multiplying $(5.25 imes 10^{-8})$ and $(4 imes 10^{3})$ in scientific notation?
What is the sum of $(1.2 imes 10^{5})$ and $(5.35 imes 10^{6})$ expressed in scientific notation?
What is the sum of $(1.2 imes 10^{5})$ and $(5.35 imes 10^{6})$ expressed in scientific notation?
Calculate the difference in distances from the sun between Mars and Jupiter, given Mars is $54,000,000$ km and Jupiter is $6.3 imes 10^{9}$ km.
Calculate the difference in distances from the sun between Mars and Jupiter, given Mars is $54,000,000$ km and Jupiter is $6.3 imes 10^{9}$ km.
If there are $2.4 imes 10^{4}$ ants for every human on the planet, approximately how many ants are there if the world population is about $7 imes 10^{9}$?
If there are $2.4 imes 10^{4}$ ants for every human on the planet, approximately how many ants are there if the world population is about $7 imes 10^{9}$?
What is the result of $(8.9 imes 10^{5})(6.5 imes 10^{6})$ expressed in scientific notation?
What is the result of $(8.9 imes 10^{5})(6.5 imes 10^{6})$ expressed in scientific notation?
In the equation $3(x - 2) = -18$, what is the value of $x$?
In the equation $3(x - 2) = -18$, what is the value of $x$?
What will the total cost be if the jacket costs $30 more than a shirt and the total for two shirts and one jacket is $150?
What will the total cost be if the jacket costs $30 more than a shirt and the total for two shirts and one jacket is $150?
If all three consecutive odd integers sum to $171$, what would be the smallest of the three integers?
If all three consecutive odd integers sum to $171$, what would be the smallest of the three integers?
Flashcards
Product of Powers Rule
Product of Powers Rule
When multiplying powers with the same base, keep the base and add the exponents.
Power of a Power Rule
Power of a Power Rule
When raising a power to another power, multiply the exponents.
Zero Power Rule
Zero Power Rule
Any number raised to the power of zero equals 1.
Quotient of Powers Rule
Quotient of Powers Rule
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Scientific Notation
Scientific Notation
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Multiplying Scientific Notation
Multiplying Scientific Notation
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Dividing Scientific Notation
Dividing Scientific Notation
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Adding/Subtracting Scientific Notation
Adding/Subtracting Scientific Notation
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Multiplying Numbers in Scientific Notation
Multiplying Numbers in Scientific Notation
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Adding Numbers in Scientific Notation
Adding Numbers in Scientific Notation
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Equation
Equation
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Solution to an Equation
Solution to an Equation
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Inequality
Inequality
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System of Equations
System of Equations
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Solution to a System of Equations
Solution to a System of Equations
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Study Notes
Exponents and Scientific Notation
- Rules for Exponents
- (xa)(xb) = xa+b
- (xa)b = xab
- x0 = 1
- xa/xb = xa-b
Evaluating Expressions
-
Example 1
- 52 = 25
- (-3)3 = -27
- -24 = -16
- 60 = 1
-
Example 2
- 23 x (-3)2 = 8 x 9 = 72
- 3-2 = 1/9
- (-2)-3 = 1/-8 = -1/8
- (1/2)2 = 1/4
- (-3)2 = 9
-
Example 3
- (-3)3 = -27
- -40 = -1
- 42 x 45 = 47
- 24 x 8 = 24 x 23 = 27
- 86/84 = 82
- (53)2 = 56
-
Example 4 (-5)3 x (-5)-6 = (-5)-3 = 1/-125 = -1/125
-
Example 5 (42 x 34)5 = 410 x 320
-
(32)-2 = 3-4 = 1/81
-
Example 6 25/53 = 52/53 = 1/5
Scientific Notation
- Form: a x 10b (where 1 ≤ a < 10 and b is an integer)
- Examples
- 45,000,000 = 4.5 x 107
- 0.00034 = 3.4 x 10-4
- 870,000 = 8.7 x 105
- 0.0000016 = 1.6 x 10-6
Equations and Inequalities
- Solving Equations
- isolate the variable using inverse operations.
- Distribute when needed
- Combine like terms
Graphing
- Parallel to Axis
- Horizontal lines are parallel to the x-axis
- Vertical lines are parallel to the y-axis
Graphing
- Slope-intercept form: y = mx + b
- m is the slope, b is the y-intercept
Systems of Equations
- Methods: Substitution, elimination or graphing.
- Graphing requires plotting equations onto a graph and identifying the point of intersection.
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Description
Test your understanding of exponents and scientific notation with this quiz. Explore the rules and evaluate various expressions to see how well you grasp these concepts. Perfect for reinforcing your knowledge in mathematics!
