Top and bottom
The outside power applies to every factor — both the numerator and the denominator.
Why it works
(x/y)(x/y)(x/y) = x³/y³.
Powers · Power of a power · 5.3
Power of a quotient.
A power of a fraction raises both the top and the bottom: (x/y)ⁿ = xⁿ/yⁿ. (x/y)³ = x³/y³.
See it work.
Watch the method
Power of a quotient
(x/y)³ = x³/y³.
1
Raise EACH factor
A power of a product hits every factor — including the coefficient.
2
Apply the power
Raise each factor to the outside power.
Practice until it feels automatic.
Your turn
Work it out.
Type with ^ for powers — e.g. x^5.
streak 0
best 0
… =
The idea underneath.
From easy to tricky.
Simplify (x/y)^2
1
Raise EACH factor
A power of a product hits every factor — including the coefficient. (x ÷ y)^2
2
Apply the power
Raise each factor to the outside power. = \fracx^2y^2
Simplify (x/y)^2
1
Raise EACH factor
A power of a product hits every factor — including the coefficient. (x ÷ y)^2
2
Apply the power
Raise each factor to the outside power. = \fracx^2y^2
Simplify (x/y)^3
1
Raise EACH factor
A power of a product hits every factor — including the coefficient. (x ÷ y)^3
2
Apply the power
Raise each factor to the outside power. = \fracx^3y^3
Where students slip.
Trap
Raising only the top.
Fix
The bottom gets the power too.
Trap
Forgetting a coefficient on top or bottom.
Fix
Every factor is raised.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
Simplify (x/y)^3
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
C2
Simplify (x/y)^2
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
C3
Simplify (x/y)^3
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
C4
Simplify (x/y)^2
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
Apply
Apply (4)
A1
Simplify (x/y)^3
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
A2
Simplify (x/y)^3
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
A3
Simplify (x/y)^3
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
A4
Simplify (x/y)^2
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
Extension
Extension (4)
E1
Simplify (x/y)^2
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
E2
Simplify (x/y)^3
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
E3
Simplify (x/y)^3
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.
E4
Simplify (x/y)^2
Need a hint?
- Raise the top and the bottom.
- Apply the exponent to each.