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Questions and Answers
Evaluate $5^2$.
Evaluate $5^2$.
25
What is the result of $(-3)^3$?
What is the result of $(-3)^3$?
-27
Simplify $4^2 imes 4^5$ using exponent rules.
Simplify $4^2 imes 4^5$ using exponent rules.
4^7
What is $-2^{-3}$ simplified?
What is $-2^{-3}$ simplified?
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Convert 45,000,000 to scientific notation.
Convert 45,000,000 to scientific notation.
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Write the number 0.00034 in scientific notation.
Write the number 0.00034 in scientific notation.
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Perform the operation $(4x^2y)(-2xy^3)$ and simplify.
Perform the operation $(4x^2y)(-2xy^3)$ and simplify.
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What is the result of $(-3x^2y^4)/(12x^8y^3)$?
What is the result of $(-3x^2y^4)/(12x^8y^3)$?
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Perform the operation (5.25 x 10^(-8)) x (4 x 10^3) and express your answer in scientific notation.
Perform the operation (5.25 x 10^(-8)) x (4 x 10^3) and express your answer in scientific notation.
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Calculate (3.4 x 10^(-8)) x (8 x 10^5) and give the answer in scientific notation.
Calculate (3.4 x 10^(-8)) x (8 x 10^5) and give the answer in scientific notation.
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What is the result of adding (1.2 x 10^5) + (5.35 x 10^6) in scientific notation?
What is the result of adding (1.2 x 10^5) + (5.35 x 10^6) in scientific notation?
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How many ants are in the world if there are 2.4 x 10^4 ants for every human, with a world population of approximately 7 billion?
How many ants are in the world if there are 2.4 x 10^4 ants for every human, with a world population of approximately 7 billion?
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Find the difference between the distances of Mars (54,000,000 km) and Jupiter (6.3 x 10^9 km) from the sun in scientific notation.
Find the difference between the distances of Mars (54,000,000 km) and Jupiter (6.3 x 10^9 km) from the sun in scientific notation.
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Solve for x in the equation 3(x - 2) = -18.
Solve for x in the equation 3(x - 2) = -18.
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In the equation 5y - 4 = 2y + 5, what is the value of y?
In the equation 5y - 4 = 2y + 5, what is the value of y?
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What is the sum of three consecutive odd integers that equals 171?
What is the sum of three consecutive odd integers that equals 171?
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Study Notes
Exponents and Scientific Notation
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Rules for Exponents:
- (xa)(xb) = xa+b
- (xa)b = xab
- x0 = 1
- xa/xb = xa-b
Evaluate Expressions
- 52 = 25
- (-3)3 = -27
- -24 = -24
- 60 = 60
- 23 x (-3)2 = 8 x 9 = 72
- -16 = -16
- 3-2 = 1/9
- (-2)-3 = 1/(-8) = -1/8
- (1/2)2 = 1/4
- (-3)2 = 9
Simplify Using Exponents
- 42 x 45 = 47
- 24 x 8 = 24 x 23= 27
- 86 / 84 = 82
- (53)2 = 56
- (-5)3 x (-5)-6 = (-5)-3 = -1/125
- 25 / 53= 25/125 = 1/5
- (42 x 34)5 = 410 x 320
- (32)-2 = 3-4 = 1/81
Perform Indicated Operations
- (4x2y3)(-2x5y2) = -8x7y5
- (-3x4y2)2 = 9x8y4
- (12x8y3)/(-3x10y) = -4x-2y2 = -4y2/x2
Scientific Notation
- a x 10b where 1 ≤ a < 10
- To multiply numbers in scientific notation, multiply the coefficients and add the exponents.
- To divide numbers in scientific notation, divide the coefficients and subtract the exponents.
- When adding or subtracting numbers in scientific notation, the powers of 10 must be the same.
Write Numbers in Scientific Notation
- 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
Write Numbers in Standard Form
- 5.24 x 104 = 52,400
- 3.02 x 10-5 = 0.0000302
- 7.3 x 108 = 730,000,000
Perform Indicated Operations in Scientific Notation
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(5.25 x 102) x (4 x 103) = 21 x 105 = 2.1 x 106
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(3.4 x 108) x (8 x 105) = 27.2 x 1013 = 2.72 x 1014
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(1.2 x 105) + (5.35 x 106) = 12000 + 5350000 = 5362000 = 5.362 x 106
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(8.9 x 105)(6.5 x 106) = 57.85 x 1011 = 5.785 x 1012
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(3.5 x 109)/(1.4 x 10-3) = 2.5 x 109-(-3) = 2.5 x 1012
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(5.1 x 1012) – (6.3 × 109) = 5100000000000 - 6300000000 = 5.037 x 1012
World Population and Ants
- Approximately 7 x 109 people
- 2.4 x 104 ants per human
- Total ants: 1.68 x 1014
Mars and Jupiter Distance
- Mars: 54,000,000 km = 5.4 x 107 km
- Jupiter: 6.3 x 108 km
- Difference: 5.76 x 108 km.
Equations and Inequalities
- Solve for the variables of the given equations, using algebraic methods.
Graphing
- y = 3 is parallel to the x-axis
- Equation of a line parallel to the x-axis and through (2, 6) is y = 6
- Equation of a line with undefined slope through (4, -6) is x = 4
- Point (4, 5) lies on the line y = 1/2x - 6 is verified by substitution.
Systems of Equations
- Solving systems of equation algebraically: substitution or elimination methods
- Solving systems of equation graphically.
- Determining coordinate points on graphs from different equations.
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Description
Test your understanding of the rules and evaluation of exponents and scientific notation in mathematics. This quiz covers simplification techniques and various expressions involving exponents. Perfect for reinforcing your algebra skills!
