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Questions and Answers
Simplify the expression (–7x^2)(3x^5)
Simplify the expression (–7x^2)(3x^5)
Which of the following expressions represents the volume of a rectangular prism with length 5x, width 2x, and height 3x^2?
Which of the following expressions represents the volume of a rectangular prism with length 5x, width 2x, and height 3x^2?
What is the simplified form of (-3x^2)(2x^3)(-x^4)?
What is the simplified form of (-3x^2)(2x^3)(-x^4)?
Which expression is equivalent to 3x^½?
Which expression is equivalent to 3x^½?
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Simplify the expression √(8x^3)
Simplify the expression √(8x^3)
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Flashcards
Monomial
Monomial
An algebraic expression with one term.
Scientific Notation
Scientific Notation
A way to express large numbers using powers of ten.
Volume of a Solid
Volume of a Solid
The amount of space occupied by a 3D object, expressed as monomial if uniform.
Properties of Exponents
Properties of Exponents
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Radical and Exponential Form
Radical and Exponential Form
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Study Notes
Simplifying Expressions
- Product of Powers: Multiplying terms with the same base: Add the exponents. Example: y5 * y = y6
- Power of a Power: Raising a power to another power: Multiply the exponents. Example: (n2)7 = n14
- Power of a Product: To find the power of a product, find the power of each factor in the product. Example ( (-7x²) (x4) = -7x6
- Simplify expressions with multiple variables: Simplify each variable separately using the rules above. Example: -3x(x²)(x4) = -3x7
Operations with Monomials
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Multiplying Monomials: Multiply the coefficients and add the exponents of like variables. Example: (-3j2k3)2(2j2k)3 = 36j10k9
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Raising a Monomial to a Power: Raise each factor (coefficient and variables) to the given power. Example: (25a2b)3(ab)2 = 15625a8b5
Volume of Rectangular Prisms as Monomials
- Volume: The area of the base multiplied by the height. Example: The volume in the image is m4n2
Determining if an Expression is a Monomial
- A monomial is a single term with a coefficient and variables raised to whole number exponents. A-b and p2/r2 are not monomials
Simplifying Expressions Involving Fractions
- Simplify the numerator and denominator separately. Example: (32x3y2z5)/(-8xyz2)
Exponential Expressions
- Negative Exponents: A negative exponent indicates a reciprocal. Example: a-5 = 1/a5
- Zero Exponents: Any non-zero number raised to the zero power equals 1. Example: a0 = 1
- Simplify Expressions with Negative Exponents Example: -20t-1u-4/4tu-3 = -5/t
Converting Between Exponential and Radical Forms
- Exponential to Radical: Example: 301/2 = √30
- Radical to Exponential: Example: √16 = 161/2
Evaluating Expressions
- Follow order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Example ∛32 = 2x5-3 = 10 -3 =7
Scientific Notation
- Convert large numbers: Express a number greater than 10 or less than 1 as a product of a number between 1 and 10 and an integer power of 10. Example: 92,900,000 = 9.29 x 107
- Divide numbers in scientific notation: Use rules for exponents. Example: (9.29 x 107)/(6.41 x 107) ≈ 1.45
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Description
Test your understanding of simplifying algebraic expressions and operations with monomials. This quiz covers rules such as the product of powers, power of a power, and multiplication of monomials. Prepare to apply these concepts through various examples.
