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Questions and Answers
When dividing terms with the same base but different exponents, which operation is performed on the exponents?
When dividing terms with the same base but different exponents, which operation is performed on the exponents?
- The exponents are multiplied.
- The exponents are subtracted. (correct)
- The exponents are added.
- The exponents remain unchanged.
Simplify the expression: $\frac{9x^7}{3x^3}$
Simplify the expression: $\frac{9x^7}{3x^3}$
- $6x^{4}$
- $6x^{10}$
- $3x^{4}$ (correct)
- $3x^{10}$
Which of the following is the correct first step when simplifying an expression like $\frac{12a^8}{4a^2}$?
Which of the following is the correct first step when simplifying an expression like $\frac{12a^8}{4a^2}$?
- Multiply the coefficients and add the exponents.
- Rewrite the expression as a product of two fractions. (correct)
- Add the coefficients (12 and 4).
- Subtract the exponents from the coefficients.
What is the simplified form of the expression $\frac{5m^{12}}{m^4}$?
What is the simplified form of the expression $\frac{5m^{12}}{m^4}$?
After splitting the original expression into numerical and variable fractions, what is the next step in simplifying $\frac{15y^{9}}{3y^{3}}$?
After splitting the original expression into numerical and variable fractions, what is the next step in simplifying $\frac{15y^{9}}{3y^{3}}$?
Flashcards
Divisional Law
Divisional Law
A rule for simplifying fractions with the same base but different indices by subtracting the exponent in the denominator from the exponent in the numerator.
Fraction with Same Base
Fraction with Same Base
A mathematical expression where two terms share the same base but have different exponents, enabling simplification using Divisional Law.
Example of Divisional Law
Example of Divisional Law
When dividing 10^6 by 10^2, you get 10^(6-2) = 10^4.
Rewriting a Fraction
Rewriting a Fraction
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Simplifying with Indices
Simplifying with Indices
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Study Notes
Divisional Law
- Division applies when a fraction has the same base but different exponents.
- Subtract the smaller exponent from the larger exponent.
- Example: 10⁶ / 10² = 10⁴
Fractions with Variables
- Rewrite division as a fraction
- Separate variables and constants
- Apply the rule of exponents to simplify by subtracting exponents where the base is the same
- Example: 8b¹⁰ / 2b⁶ = (8/2) * (b¹⁰/b⁶) = 4b⁴
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Description
Learn how to divide expressions with the same base but different exponents. Review how to handle variables and constants in fractions, applying the rule of exponents to simplify expressions.
