Exponents & Radicals ​​​​​(GMAT Course – Problem Solving & Data Sufficiency Math Concepts)

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Exponents & Radicals ​​​​​(GMAT Course, Segment 2–Problem Solving & Data Sufficiency Math Concepts)
Exponential Notation Defined
- Base is numeric value
- Exponent is number of times numeric value is multiplied by itself
- 2^4 = 2×2×2×2 = 16
- Only Negative Base Raised to an Odd Power Can Produce Value less than 0
- (−2)^2 = −2×−2 = 4 | −2^3 = −2×−2×−2 = −8
Radical Notation Defined
- Radicand is numeric value
- Degree is number of times root value is multiplied by itself to produce the radicand
- ∛64=4 | Because 4 × 4 × 4 = 64
- Cannot square root value less than 0 as √(−1)=𝑖 | Not allowed for GMAT

Manipulating Exponents with Same Bases
- Multiplying Bases → Add Exponents
- 4^3 × 4^4 = 4^7
- Dividing Bases → Subtract Exponents
- 4^4 ÷ 4^3 = 4^1=4
- Raising Base to New Power → Multiply Exponents
- (4^4)2 = 4^8
- Adding or Subtracting Bases → Factor Before Manipulating
- 4^2 + 4^2 + 4^2 + 4^2
- 4^2 (1+1+1+1)
- 4^2×4 = 4^3 = 4×4×4 = 64

Manipulating Constant Exponents
- Multiply Bases as Normal
- 2^2×5^2 = 10^2
- 4×25 = 100
- Divide Bases as Normal
- 6^2÷3^2 = 2^2
- 36÷9 = 4
- Factor Bases as Normal
- (8^2+6^2)=64+36=100
- 2^2 (4^2+3^2 ) = 4(16+9) = 4×25 = 100

Manipulating Constant Radicals
- Multiply Radicands as Normal
- √16×√9 = √144
- 4×3 = 12
- Divide Radicands as Normal
- √144÷√36 = √4
- 12÷6 = 2
- √80÷√5 = √16 = 4
- Factor Perfect Squares to Simplify
- √72 = √(36×2) = 6√2

Exponents & Radicals ​​​​​(GMAT Course, Segment 2–Problem Solving & Data Sufficiency Math Concepts)
0:00 Introduction
0:15 Exponential Notation
1:53 Radical Notation
4:13 Exponential Notation Continued
6:43 Manipulating Exponents with Same Bases
9:37 Manipulating Constant Exponents
11:18 Manipulating Constant Radicals
14:44 Example 1
18:26 Example 2

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