Questions and Answers
What is the value of $3^4$ and how can you express this using exponents?
The value of $3^4$ is 81, which can be expressed as $3 imes 3 imes 3 imes 3$.
Convert the rational number $ rac{7}{3}$ to a decimal and explain why it is considered rational.
The decimal form of $ rac{7}{3}$ is approximately 2.33, and it is rational because it can be expressed as a fraction of two integers.
If $x = 4$, what is the value of $2^{x-1}$ and how does it demonstrate properties of exponents?
If $x = 4$, then $2^{x-1} = 2^{3} = 8$, demonstrating that when the exponent is reduced by 1, it results in half the original power.
How do you calculate the area of a rectangle when given the lengths of two sides using the properties of quadrilaterals?
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Describe the relationship between a square and a rectangle in terms of their properties as quadrilaterals.
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Study Notes
Exponentiation
- The value of (3^4) is 81, calculated as (3 \times 3 \times 3 \times 3).
- This expression can be written using exponents as (3^4), indicating the base (3) multiplied by itself four times.
Rational Numbers
- The rational number (\frac{7}{3}) converts to a decimal as approximately 2.3333 (repeating).
- It is considered rational because it can be expressed as a fraction, where both the numerator (7) and denominator (3) are integers.
Exponent Properties
- If (x = 4), the value of (2^{x-1}) is (2^{4-1} = 2^3), which equals 8.
- This illustrates the property of exponents where (a^{m-n} = \frac{a^m}{a^n}), showcasing how exponents can be manipulated based on algebraic expressions.
Area Calculation of Rectangles
- The area of a rectangle is calculated by multiplying the lengths of its two sides: Area = length × width.
- This property stems from the definition of quadrilaterals, where rectangles have opposite sides that are equal and angles that are right angles.
Relationship between Squares and Rectangles
- A square is a specific type of rectangle with all four sides equal in length.
- Both shapes are quadrilaterals, but a square must meet additional criteria of equal side lengths and four right angles, while a rectangle must only have four right angles with opposite sides equal.
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Description
Test your knowledge on exponents, rational numbers, and the properties of quadrilaterals. Explore calculating powers, converting fractions to decimals, and applying formulas for area in geometrical shapes. This quiz will help you understand key concepts in mathematics.
