SME
Grade 8 Math · Problem type
Zero and negative exponents
Use this for “What is 5⁻¹?” or “Write 10⁻² as a fraction.”
Table
Exponent (n)
Value (P)
This is an example. Type your own values to start a new problem.
b
=
1
5
P
Formulas
P
=
b
^
n
(value
=
baseexponent)
1
5
=
5
-1
Assumptions
•
Each time the exponent drops by 1, the value is divided by the base.
•
So b⁰ = 1 and b⁻ⁿ = 1 ÷ bⁿ.
•
A negative exponent does not make the value negative.
Step-by-step
WE KNOW
b = 5 (base), n = −1 (exponent)
FIND
value (P)
Step 1 · Find value (P)
Use P = bⁿ (value = baseᵉˣᵖᵒⁿᵉⁿᵗ)
A negative exponent is 1 divided by the power with the positive exponent.
P
=
1
5
1
5
3
=
125,
5
2
=
25,
5
1
=
5,
5
0
=
1,
5
-1
=
1
5
:
each
step
down
divides
by
5.
P
=
1
5
Check
Put the numbers back in. Both sides should match.
1
÷
5
1
=
1
5
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.