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Simplifying Variable CUBES
Contributed by: Smith
x4 • x4 • x4 =  x12
x3 • x3 • x3 =  x9
x  •  x  •  x  =  x3
x2 • x2 • x2 =  x6
Perfect CUBES
Perfect variableCubes have exponentsthat aremultiples of:
 2
 3
 4
 5
Perfect cubes with a variable base (like x),      have powers that are multiples of 3.
x2
x7
Click on ALL perfect Cubes
x3
x8
x5
x23
x42
x6
x12
x9
?
x6
?
=
=
=
x4
?
x2
?
x3
Drag the terms
 to the correct
 locations
Perfect variableCubes have exponentsthat aremultiples of 3.
Simplify the
perfect CUBE.
Bring down the
imperfect CUBE:
Rewrite
using the
GREATEST
perfect CUBE
factor:
Simplify:
x12
x4
?
x14
x2
x2
?
Simplify the
perfect CUBE.
Bring down the
imperfect CUBE:
Rewrite
using the
GREATEST
perfect CUBE
factor:
Simplify:
x36
x
x37
x1
x
Simplify the
perfect CUBE.
Bring down the
imperfect CUBE:
Rewrite
using the
GREATEST
perfect CUBE
factor:
Simplify:
x9
x
x11
x
x
Simplify the
perfect CUBE.
Bring down the
imperfect CUBE:
Rewrite
using the
GREATEST
perfect CUBE
factor:
Simplify:
x
x
x22
x
x
Simplify the
perfect CUBE.
Bring down the
imperfect CUBE:
Rewrite
using the
GREATEST
perfect CUBE
factor:
Simplify:
x
x
x8
x
x
Rewrite
using the
GREATEST
perfect CUBE
factor:
Simplify:
Simplify the
perfect CUBE.
Bring down the
imperfect CUBE:
a  x
a  x
a5x7
a  x
a  x
These are SIMPLIFIED CUBE roots.
They have NO perfect cube factors.
x2
a
a2x2
ax2
a2x
x
Click ALL SIMPLIFIED CUBE roots.
a2
x
a2
x
a2x2
ax3
a2x2
ax3
a4x
x5
x5
a4x
Purr-fect CUBE
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