Podcast
Questions and Answers
When dividing terms with the same base and different exponents, which operation is performed on the exponents?
When dividing terms with the same base and different exponents, which operation is performed on the exponents?
- The exponents are multiplied.
- The exponents are subtracted. (correct)
- The exponents remain the same.
- The exponents are added.
Simplify the expression: $\frac{15x^8}{3x^2}$
Simplify the expression: $\frac{15x^8}{3x^2}$
- $5x^4$
- $12x^{10}$
- $12x^6$
- $5x^6$ (correct)
Which of the following is the correct first step when simplifying an expression like $\frac{12a^9}{4a^3}$?
Which of the following is the correct first step when simplifying an expression like $\frac{12a^9}{4a^3}$?
- Simplifying the coefficient and ignoring the variables.
- Rewriting as a multiplication: $12 \times a^9 \times 4 \times a^3$.
- Splitting into numerical and variable fractions: $\frac{12}{4} \times \frac{a^9}{a^3}$. (correct)
- Adding the exponents: $9 + 3$.
Simplify the expression: $\frac{9y^{12}}{3y^4}$
Simplify the expression: $\frac{9y^{12}}{3y^4}$
What is the simplified form of the expression $\frac{20c^{15}}{5c^5}$?
What is the simplified form of the expression $\frac{20c^{15}}{5c^5}$?
Flashcards
Divisional Law
Divisional Law
A law for fractions with the same base, where subtracting indices determines the result.
Fraction with Same Base
Fraction with Same Base
A fraction where both the numerator and denominator share the same base but have different indices.
Simplifying a Fraction
Simplifying a Fraction
The process of breaking down a fraction to its simplest form using known rules.
Steps to Solve Division with Variables
Steps to Solve Division with Variables
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Result of 8b^10 / 2b^6
Result of 8b^10 / 2b^6
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Study Notes
Division Law of Exponents
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Division with the same base, but different exponents: Subtract the bottom exponent from the top exponent.
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Example: 106 / 102 = 10(6-2) = 104
Fractions with Variables and Exponents
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Rewrite the division problem as a fraction: numerator over denominator
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Use the rule for variables with the same base: Multiply variables with common bases (add the exponents); Divide variables with common bases (subtract the exponents)
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Example: 8b10 / 2b6 = (8/2) * (b10/b6) = 4b(10-6) = 4b4
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