Fraction Simplification

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Questions and Answers

What is the first step in simplifying a fraction's numerator?

  • Multiply the numerator by itself. (correct)
  • Identify the denominator.
  • Subtract remaining powers in numerator.
  • Combine the numerator and denominator results.

The final simplified answer of a fraction should always be in the form of $a^5 b^9$.

False (B)

What is the purpose of identifying the denominator in the simplification process?

To understand the overall structure of the fraction and categorize the powers.

To simplify the fraction, you subtract the numerator powers from the ______ powers.

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

Match the following steps with their corresponding actions in simplifying a fraction:

<p>Step 1 = Multiply the numerator by itself. Step 2 = Identify the denominator. Step 4 = Subtract numerator powers from denominator powers. Step 5 = Include the negative sign from the denominator.</p> Signup and view all the answers

What is the final result after simplifying the expression?

<p>$-a^5 b^9$ (A)</p> Signup and view all the answers

When simplifying an expression, you add the numerator powers and the denominator powers.

<p>False (B)</p> Signup and view all the answers

What operation is used to combine the results of the numerator after squaring and multiplying?

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

To simplify the expression, one must subtract the powers of the numerator from the __________.

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

Match the following terms with their definitions:

<p>Numerator = The top part of a fraction Denominator = The bottom part of a fraction Exponent = The power to which a number is raised Power = The result of multiplying a number by itself a certain number of times</p> Signup and view all the answers

Flashcards

Simplifying Fractions - Numerator

Multiply the numerator by itself repeatedly to get the numerator's power.

Simplifying Fractions - Denominator

Identify the denominator's value for the fraction.

Simplifying Fractions - Combining Steps

Combine the numerator's and denominator's powers to form the fraction.

Simplifying Fractions - Subtracting Exponents

Subtract the numerator exponents from the denominator exponents to simplify.

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Simplifying Fractions - Final Answer Format

The final answer is in the form of $a^n b^m$ (where n and m are integers representing powers). Add a - sign from denominator into final answer, if it exists.

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Simplify the expression

Rewrite the expression in its simplest form by using the rules of exponents.

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Numerator (top part)

The part of a fraction that is above the fraction bar.

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Denominator (bottom part)

The part of a fraction that is below the fraction bar.

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Subtracting exponents

When dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.

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Final answer format

The final answer is expressed as a product of powers with their respective bases and exponents.

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Study Notes

Fraction Simplification

  • Numerator: First, square the numerator. Next, multiply the numerator by itself five times. Then, multiply the results.
  • Denominator: Identify the denominator.
  • Combining: Combine the results from the numerator and denominator.
  • Simplifying: Subtract the powers in the numerator and denominator. Again, subtract the powers in the numerator and denominator.
  • Final Result: Include the negative sign that exists from the denominator. Example: a9 b5

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