Exponent rules and roots
Lesson 9 of 20 in Union Aptitude Prep. The start plays free here.
- x² means x × x
- A square root of 36: 6 × 6 = 36
- Another: (−6) × (−6) = 36
- x² × x³ = x⁵
- (x²)³ = x⁶
- 7⁰ = 1
- 2⁻³ = 1/2³ = 1/8
- √36 = 6; square roots: 6 and −6
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How the lesson starts
In x², x is the base. The raised two is the exponent. It means two factors of x multiplied together, not x times two.
A square root works backward from a square. You look for a number that, multiplied by itself, gives the starting number.
You see x squared times x cubed in your booklet. The bases match. Keep the base and add the exponents: two plus three gives five.
Then, in the full lesson
- Power outside
- Zero power
- Negative exponent
- Square roots
- 2 questions along the way
A question from this lesson
You need to simplify (y³)⁴. What should you write?
- y¹²
- y⁷
- y⁸¹
Show the answer
A. y¹². y¹² follows from multiplying three by four. y⁷ adds the exponents instead. y⁸¹ raises three to the fourth power instead of multiplying.
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Paid once, no subscription. Ask for a refund within 7 days of buying if you’ve done less than 25% of the class.
- Number series trainer
- Algebra & functions with worked steps
- Reading comprehension sets
Not affiliated with IBEW, NECA, ETA or any JATC. Original practice questions only.