SME
Grade 9 Math · Problem type
Rational exponents
Use this for “Evaluate 27²ᐟ³” or “16³ᐟ²”.
Table
Top of the exponent (p)
Value (v)
This is an example. Type your own values to start a new problem.
b
/
=
(
)
=
v
Formulas
w
=
b
1
q
3
=
27
1
3
v
=
w
p
9
=
3
2
Assumptions
•
b1/q is the qth root of b: 271/3 = ∛27 = 3.
•
bp/q is that root raised to the power p: take the root first, the numbers stay small.
•
A negative p means 1 over the power.
Step-by-step
WE KNOW
b = 27, p = 2, q = 3
FIND
the qth root of b (w), value (v)
Step 1 · Find the qth root of b (w)
Use w = b1/q
The
bottom
of
the
exponent
is
the
root:
find
the
number
that,
used
q
times
as
a
factor,
makes
b
.
w
=
∛
b
w
=
∛27
w
=
3
Step 2 · Find value (v)
Use v = wᵖ
The top of the exponent is the power: raise the root to it.
v
=
3
2
v
=
9
Check
Put the numbers back in. Both sides should match.
3 = ∛27 ✓
9
=
3
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Exponent properties, rational exponents, simplifying radicals, and rational and irrational numbers
Main lesson
Simplify a cube root
Use this for “Simplify ∛54.”
Divide monomials
Use this for “Simplify 12x⁷ ÷ 3x².”
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?”