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
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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.