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Exponents: Division Law

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Questions and Answers

Simplify the expression: $\frac{5^7}{5^3}$

$5^4$ (correct)
$5^{21}$
$5^{10}$
$1^4$

According to the division law, when dividing terms with the same base, you should add the exponents.

False (B)

Using the principle of divisional law, what is $\frac{x^{12}}{x^4}$ simplified?

x^8

When simplifying $\frac{9y^{15}}{3y^5}$, the numerical part simplifies to ______, and the variable part simplifies to $y^{10}$.

<p>3</p> Signup and view all the answers

Match the following expressions with their simplified forms using the division law:

<p>$\frac{a^9}{a^3}$ = $a^6$ $\frac{b^{12}}{b^4}$ = $b^8$ $\frac{c^5}{c^2}$ = $c^3$ $\frac{d^{10}}{d^5}$ = $d^5$</p> Signup and view all the answers

Flashcards

Divisional Law

The law used for fractions with the same base and different indices, subtracting the lower index from the upper index.

Fraction Simplification

The process of rewriting a complex fraction into simpler parts for easier calculations.

Base and Indices

In an expression like a^m/b^n, the base is 'a' and 'b', while 'm' and 'n' are their respective indices.

Rewriting Division

Expressing division as a fraction to facilitate simplification, e.g., a/b can be rewritten as a ÷ b.

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Simplest Form

The simplest way to express a mathematical expression, with no more possible simplifications (e.g., 4b^4).

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Study Notes

Divisional Law

Division of fractions with the same base and different indices involves subtracting the smaller index from the larger index, keeping the base the same.
For example, 10⁶ / 10² = 10⁴
When dealing with variables, fractions are rewritten.
Example: 8b¹⁰/2b⁶ is rewritten as (8/2) x (b¹⁰/b⁶).
Then the numerical fraction is simplified (8/2 = 4).
Similarly, the variable fraction is simplified (b¹⁰/b⁶ = b⁴).
Combining the results gives the final answer 4b⁴.

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Description

Learn about the division law of exponents. Simplify expressions with the same base by subtracting indices. Examples include both numerical and variable expressions.