SME
Grade 8 Math · Problem type
Dividing powers
Use this for “Write 7⁶ ÷ 7² with a single exponent” or “What is 10³ ÷ 10³?”
Diagram
2⁶ ÷ 2² = 2⁶⁻² = 2⁴ = 16
2 pairs cancel (2 ÷ 2 = 1).
4 factors are left on top.
This is an example. Type your own values to start a new problem.
b
÷
b
=
b
=
P
Formulas
k
=
m
−
n
(exponent
of
the
answer
=
first
exponent
−
second
exponent)
4 = 6 − 2
P
=
b
^
k
(value
of
the
answer
=
baseexponent
of
the
answer)
16
=
2
4
Assumptions
•
Each factor on top cancels one on the bottom: 7 ÷ 7 = 1.
•
So dividing powers of one base subtracts the exponents.
•
Equal exponents give b⁰ = 1. More factors on the bottom give a negative exponent.
Step-by-step
WE KNOW
b = 2 (base), m = 6 (first exponent), n = 2 (second exponent)
FIND
exponent of the answer (k), value of the answer (P)
Step 1 · Find exponent of the answer (k)
Use k = m − n (exponent of the answer = first exponent − second exponent)
Dividing powers of the same base subtracts the exponents.
k
=
6
−
2
k
=
4
Step 2 · Find value of the answer (P)
Use P = bᵏ (value of the answer = baseᵉˣᵖᵒⁿᵉⁿᵗ of the answer)
Multiply the base by itself as many times as the exponent says.
P
=
2
4
P
=
16
Check
Put the numbers back in. Both sides should match.
4 = 6 − 2 ✓
2
4
=
16
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.