Questions and Answers
What is the value of the expression $(-2)^5$?
-32
Using exponents, what is the simplified form of $\frac{15x^6}{3x^2}$?
5x^4
Using exponents, what is the simplified form of $(-2x^2y^3)^3$?
-8x^6y^9
How is the expression $10^{-3}$ written using a positive exponent?
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The Washington Monument weighs approximately 90,800 tons. What is this number written in scientific notation?
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What is the value of the expression $-(\sqrt{198}/81)$?
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To the nearest whole number, what is the best estimate of $\sqrt{444}$?
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Which of the following is equivalent to $-\frac{13}{40}$?
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Which of the following is equivalent to 0.45 (repeated)?
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The area of a square ice rink is 404 square yards. To the nearest yard, what is the perimeter of the rink?
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Which number best represents the point graphed on the number line?
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For a fundraiser, the basketball team is selling 75 wristbands for $3 each. The wristbands cost a total of $37.50. If they sell all of the wristbands, how much money will be raised by the team?
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In a recent year, there were about 400,000,000 mobile internet users. That same year, there were about $1.2 \times 10^9$ desktop internet users. About how many times larger was the number of desktop internet users than the number of mobile internet users?
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Natasha is seeding her backyard. The backyard is square in shape and has an area of 4,225 square feet. What is the length of one side of Natasha's backyard?
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Name a number that is not a whole number, a number that is not an integer, a number that is not a rational number, and a number that is not an irrational number. Do not use the same number twice.
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What is the value of 1,000 cubed?
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Estimate 30 cubed to the nearest whole number.
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Solve the equation $x^2=900$.
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Graph $32^2$ on the number line.
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Simplify $[(4^3)^2]^4$.
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Study Notes
Exponent Expressions
- The value of (-2)^5 is -32.
- Simplifying 15x^6/3x^2 results in 5x^4.
- The expression (-2x^2y^3)^3 simplifies to -8x^6y^9.
- The expression 10^-3 can be rewritten using a positive exponent as 1/10^3.
Scientific Notation and Estimation
- The Washington Monument's weight of approximately 90,800 tons is expressed in scientific notation as 9.08x10^4.
- The value of -(√198)/81 equates to -14/9.
- To estimate the square root of 444, the nearest whole number is 21.
- The equivalent of -13/40 is -0.325.
- The repeating decimal 0.45 is equivalent to the fraction 5/11.
Geometry and Fundraising
- The perimeter of a square ice rink with an area of 404 square yards is approximately 80 yards.
- The basketball team's total revenue from selling 75 wrist bands at $3 each, after considering the cost of $37.50, would be $87.50.
- Natasha's square backyard has an area of 4,225 square feet, making each side approximately 33 feet long.
Internet User Statistics
- In a recent year, there were about 400 million mobile internet users, while desktop users totaled approximately 1.2 billion (1.2 x 10^9). Desktop users were roughly 3x10^1 (or 30) times more than mobile users.
Number Properties
- Various numbers highlight different properties:
- Pi (≈3.14) is not a whole number.
- 30.15 is not an integer.
- 1/2 is not a rational number.
- 18.1819181999 is not an irrational number.
- 180 is not an irrational number.
Mathematical Values
- The value of 1,000 cubed is 1,000,000,000.
- Estimating 30 cubed yields a result of approximately 27,000, which rounds to the nearest whole number of 3.
- The solutions for the equation x^2 = 900 are 30 and -30.
- Graphing 32 squared on the number line places it between the integers 5 and 6.
- The expression [(4^3)^2]^4 simplifies to 16777216^8.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of exponents with these flashcards designed for Form 2B. Each card presents a problem related to exponent rules and simplifications. Perfect for quick reviews or study sessions before exams.
