Zero and Negative Exponents
I can read zero and negative exponents correctly and rewrite them without a minus.
The problem this sheet solves
x to the negative two is one over x squared, not negative x squared. The symbol looks like a sign, so students treat it like one, and the resulting answer has the wrong magnitude AND the wrong sign. The companion error is scope: in 3x to the negative two, the exponent belongs to the x only, so the 3 stays on top. This sheet defines a negative exponent as a MOVE ACROSS THE FRACTION BAR, which is what makes it impossible to confuse with a sign, and it settles the case numerically by testing at x = 2 where a quarter and negative four cannot be mistaken for each other. What an exponent is attached to is treated as its own idea.
The key rule
A negative exponent inverts: x−2 = 1 ÷ x². It does not make anything negative. And an exponent applies only to what it is attached to, so 3x−2 keeps its 3 on top.
Negative exponent: flip it, do not negate it.
Watch out
The mistake: A student writes x−2 = −x², reading the minus as a sign.
The fix: x−2 = 1 ÷ x². Test it at x = 2: the real value is a quarter, and −x² is −4. A negative exponent moves a factor across the fraction bar; it never changes its sign.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.