SME
Grade 9 Math · Problem type
Divide monomials
Use this for “Simplify 12x⁷ ÷ 3x².”
Diagram
12x⁷
3x²
=
4x⁵
12
3
=
4;
2
pairs
of
x
cancel,
leaving
5
x's
on
top
This is an example. Type your own values to start a new problem.
a
x
÷
b
x
=
c
x
x
Value of x to check
example
y
Both sides at x
worked out (not typed)
Formulas
c
=
a
b
4
=
12
3
k
=
m
−
n
5 = 7 − 2
y
=
c
×
x
k
128
=
4
×
2
5
y
=
c
when
k
is
0
128 = 4 when 5 is 0
Assumptions
•
Divide the numbers in front, and subtract the exponents of x: xᵐ ÷ xⁿ = xᵐ⁻ⁿ.
•
A negative exponent means 1 over the power: x⁻² = 1/x².
•
Check: the answer and the first expression agree at any x, such as x = 2.
Step-by-step
WE KNOW
a = 12, m = 7, b = 3, n = 2, x = 2
FIND
number in front of the answer (c), exponent of the answer (k), both sides at x (y)
Step 1 · Find number in front of the answer (c)
Use c = a ÷ b
Divide the numbers in front.
c
=
12
3
c
=
4
Step 2 · Find exponent of the answer (k)
Use k = m − n
Dividing
powers
of
x
subtracts
the
exponents.
k
=
7
−
2
k
=
5
→
4
x
⁵
Step 3 · Find both sides at x (y)
Use y = c × xᵏ
Check:
put
x
into
the
answer;
the
first
expression
gives
the
same
value
there.
y
=
4
×
2
5
y
=
4
×
32
y
=
128
Check
Put the numbers back in. Both sides should match.
4
=
12
3
✓
5 = 7 − 2 ✓
128
=
4
×
2
5
✓
128
=
12
×
2
7
3 ×
2
2
✓
Topic check
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Related lessons
Exponent properties, rational exponents, simplifying radicals, and rational and irrational numbers
Main lesson
Simplify a cube root
Use this for “Simplify ∛54.”
Rational exponents
Use this for “Evaluate 27²ᐟ³” or “16³ᐟ²”.
Multiply square roots
Use this for “Simplify √6 × √15.”
Rational or irrational?
Use this for “Which of these are irrational: √49, 5√2, √8 × √2, π ÷ 2?”