Podcast
Questions and Answers
What is the value of $(bc^3)^0$ in the given expression?
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?
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?
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?
What is the final simplified expression after performing all operations?
What operation is performed first in the expression before simplifying?
What operation is performed first in the expression before simplifying?
Flashcards
Any number raised to the power of 0
Any number raised to the power of 0
Any number raised to the power of 0 equals 1.
Exponent
Exponent
The exponent of a number indicates how many times the base is multiplied by itself.
Coefficient
Coefficient
In algebraic expressions, coefficients are the numerical factors that multiply variables.
Power of a number
Power of a number
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Multiplying exponents with the same base
Multiplying exponents with the same base
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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
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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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