SME
Grade 8 Math · Expressions & Equations
Integer exponent rules
Use this for “Write 2³ × 2⁴ as a single power of 2, then find its value.”
Diagram
2³ × 2⁴ = 2³⁺⁴ = 2⁷ = 128
3 factors of 2 and 4 more make 7 factors.
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)
7 = 3 + 4
P
=
b
^
k
(value
of
the
answer
=
baseexponent
of
the
answer)
128
=
2
7
Assumptions
•
A power is its base used as a factor again and again: 2³ = 2 × 2 × 2.
•
Multiplying two powers of one base puts their factors in one row: add the exponents.
•
The bases must be the same: 2³ × 5² has no single exponent.
Step-by-step
WE KNOW
b = 2 (base), m = 3 (first exponent), n = 4 (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)
Multiplying powers of the same base adds the exponents.
k
=
3
+
4
k
=
7
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
7
P
=
128
Check
Put the numbers back in. Both sides should match.
7 = 3 + 4 ✓
2
7
=
128
✓
Topic check
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More problem types
Dividing powers
Use this for “Write 7⁶ ÷ 7² with a single exponent” or “What is 10³ ÷ 10³?”
A power of a power
Use this for “Write (10⁷)² with a single exponent.”
Zero and negative exponents
Use this for “What is 5⁻¹?” or “Write 10⁻² as a fraction.”
True or false?
Use this for “Is 3⁴ × 3⁵ = 3⁹ true?” or “Which equations are true?”