Evaluate exponents

key notes :

🔹 What is an Exponent?

• An exponent tells us how many times a number (the base) is multiplied by itself.
• General form: aⁿ=a×a×a…×a (n times)
• a → base
• n → exponent (or power)
• Example: 3⁴=3×3×3×3=81

🔹 Important Rules of Exponents

Product of Powers Rule:

• a^m×aⁿ=a^m+n
• Example: 2³×2⁴=2⁷=128

Quotient of Powers Rule:

• a^m/aⁿ=a^m−n (a≠0)
• Example: 5⁶/5²=5⁴=625

Power of a Power Rule:

• (a^m)ⁿ=a^m⋅n
• Example: (3²)⁴=3⁸=6561

Power of a Product Rule:

• (ab)ⁿ=aⁿ.bⁿ
• Example: (2×3)⁴=2⁴×3⁴=16×81=1296

Power of a Quotient Rule:

• (a/b)ⁿ=aⁿ/bⁿ (b≠0)
• Example: (4/5)²=16/25​

Zero Exponent Rule:

• a⁰=1 (a≠0)
• Example: 7⁰=1

Negative Exponent Rule:

• a⁻ⁿ=1/aⁿ (a≠0)
• Example: 2⁻³=1/2³=1/8

🔹 Evaluating Exponents (Examples)

• 2⁵=2×2×2×2×2=32
• (5³)²=5⁶=15625
• 7⁴/7²=7⁴⁻²=7²=49
• 10⁻²=1/10²=1/100
• (3×2)³=3³×2³=27×8=216

🔹 Common Mistakes to Avoid

a^m+aⁿ≠a^m+n

(a+b)²≠a²+b² (it is a²+2ab+b²)

Negative sign matters:

• (−2)⁴=16
• −2⁴=−16

🔹 Real-Life Applications of Exponents

• Scientific notation (large and small numbers).
• Growth and decay problems (population growth, bacteria growth, radioactive decay).
• Area and volume calculations.
• Computer science (binary numbers and memory size like KB, MB, GB).

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✅ Summary:

• Exponents are repeated multiplication.
• Learn and apply exponent rules correctly.
• Be careful with signs, brackets, and negative powers.

Learn with an example

Let’s practice!🖊️