SME
Grade 11 Math · Problem type
Rational exponents
Use this for “Evaluate 82/3”, “Graph y = 2x−1/2” or “Solve x3/2 = 27.”
Chart
Domain: all real numbers
f(8) = 4
This is an example. Type your own values to start a new problem.
y
=
a
·
x
/
Formulas
y
=
a
×
x
p
q
4
=
1
×
8
2
3
Assumptions
•
xp/q is the qth root of x, raised to the power p: 82/3 = (∛8)² = 4.
•
A negative p puts the power under 1, x−p/q = 1 ÷ xp/q, so x = 0 has no value.
•
To solve for x, divide by a and raise both sides to q/p, the reciprocal power; here x ≥ 0.
Step-by-step
WE KNOW
x = 8, a = 1, p = 2, q = 3
FIND
output (y)
Step 1 · Find output (y)
Use y = a × xp/q
Take
the
qth
root
of
x
,
raise
it
to
the
power
p
,
then
multiply
by
a
.
y
=
1
×
8
2
3
y
=
1
×
(∛8)
2
y
=
1
×
2
2
y
=
4
Check
Put the numbers back in. Both sides should match.
4
=
1
×
8
2
3
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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