Algebra Class: Simplifying Expressions
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Questions and Answers

What is the value of $(bc^3)^0$ in the given expression?

  • $0$
  • $b + c + 3$
  • $1$ (correct)
  • $bc^3$

    • What is the coefficient of the variable $a$ in the simplified form of the expression?

  • $5$
  • $-1$
  • $-5$
  • $10$ (correct)

    • Which variable's exponent will be negative after simplifying the expression?

  • $c$
  • $b$ (correct)
  • $d$
  • $a$

    • What is the final simplified expression after performing all operations?

    <p>$10a^{-1}b^{3}c$ (A)</p> Signup and view all the answers

    What operation is performed first in the expression before simplifying?

    <p>Evaluation of $(bc^3)^0$ (A)</p> Signup and view all the answers

    Flashcards

    Any number raised to the power of 0

    Any number raised to the power of 0 equals 1.

    Exponent

    The exponent of a number indicates how many times the base is multiplied by itself.

    Coefficient

    In algebraic expressions, coefficients are the numerical factors that multiply variables.

    Power of a number

    When a number is raised to a certain power, the exponent indicates how many times the base is multiplied by itself.

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    Multiplying exponents with the same base

    When multiplying exponents with the same base, you add the powers together.

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    Study Notes

    Simplifying the Expression

    • The given expression is a complex fraction involving variables and exponents.
    • To simplify the expression, we must follow the rules of exponents and the order of operations.

    Simplifying Terms with Exponents

    • Evaluate the exponent in the numerator: (2b)² = 2² * b² = 4b²

    • The expression becomes: $$\frac{\left(5ab^2c\right)\left(4b^2\right)}{\left(-2ab\right)\left(bc^3\right)^0}$$

    • Recognize that any nonzero number raised to the power of zero is equal to one. Thus, (bc³)⁰ = 1.

    • The expression simplifies to: $$\frac{\left(5ab^2c\right)\left(4b^2\right)}{\left(-2ab\right)\left(1\right)}$$

    Multiplying Terms

    • Perform the multiplications in the numerator: 5ab²c * 4b² = 20ab²(b²c) = 20ab³c

    • Perform the multiplication in the denominator: -2ab * 1 = -2ab

    • The expression becomes: $$\frac{20ab^{3}c}{-2ab}$$

    Canceling Common Factors

    • Identify common factors in the numerator and denominator:
    • 20 and -2 are both divisible by 2. 20 / -2 = -10
    • a is in both the numerator and denominator
    • b³ and b are both divisible by b. b³/b = b²
    • Thus: $$\frac{20ab^3c}{-2ab} = \frac{(-10)ab^3c}{(-1)ab} = -10b^2c$$

    Final Answer

    • The simplified expression is:
    • 10b²c

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    Description

    This quiz focuses on the simplification of complex algebraic expressions involving variables and exponents. It covers the rules of exponents, multiplication of terms, and canceling common factors to achieve the simplified form of the expression.

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