Raising a Fraction to a Power

🔑 Key Concepts

• An exponent tells how many times a base is multiplied by itself.
• When a fraction is inside parentheses, the exponent applies to the numerator and denominator.
• You can raise a fraction to a power by raising both parts of the fraction to that power.
• Parentheses matter because they show exactly what the exponent is attached to.
• Without parentheses, the exponent only applies to the number directly next to it.

✏️ Worked Examples — Raising Fractions to a Power

🧠 Math Vocabulary

• Exponent: A small number that tells how many times the base is used as a factor.
• Base: The number or expression being multiplied repeatedly.
• Power: An expression made of a base and an exponent.
• Expanded Form: Writing repeated multiplication out in full.
• Parentheses: Symbols that group numbers together to show what an exponent applies to.

💡 Main Idea

Raising a fraction to a power means multiplying that fraction by itself repeatedly. When the entire fraction is inside parentheses, the exponent applies to both the numerator and denominator. Paying attention to parentheses helps students avoid common mistakes and understand exactly what is being raised to a power.

📚 What You Should Already Know

Before working with fractions and exponents, students should understand basic exponent notation, repeated multiplication, and how to multiply fractions. It also helps to know that exponents only apply to the expression they are attached to.

🚀 What Comes Next

Next, students can compare exponential form and expanded form, work with negative bases in parentheses, and simplify more complex expressions involving exponents and fractions. These ideas also prepare students for scientific notation and algebraic expressions later on.

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