Algebra 1 · Unit 6
Simplify ratios of monomials with one or more variables. Leave positive exponents.
Jump to section:
Split the fraction
Write the coefficients as one fraction and each base as its own fraction, then simplify.
Subtract exponents
Same base in a quotient: subtract. A leftover negative exponent is a reciprocal.
More than one variable
Treat x and y separately. They are different bases.
Positive exponents in the answer
Move a factor with a negative exponent across the fraction bar so every exponent is positive.
One variable. Subtract exponents. Reduce the coefficient.
123reduce = 4
x⁷x² = x⁵
4x⁵
Answer: 4x⁵
y8−3 = y⁵
Answer: y⁵
102reduce = 5
a²
5a²
Answer: 5a²
99reduce = 1
m⁴
Answer: m⁴
x²y²
Answer: x²y²
155reduce = 3
n⁰ = 1
3
Answer: 3
Two variables, or a negative exponent that moves.
186reduce = 3
x³
y2−5 = y⁻³
3x³y⁻³
3x³y³
Answer: 3x³y³
82reduce = 4
a³
b⁻²
4a³b²
Answer: 4a³b²
x-2−3 = x⁻⁵
1x⁵
Answer: 1x⁵
248reduce = 3
m⁴
n⁰ = 1
3m⁴
Answer: 3m⁴
4x⁶y²
Answer: 4x⁶y²
124reduce = 3
x⁻³y
3yx³
Answer: 3yx³
A power outside a fraction, or several negative exponents.
(2x²y⁻¹)³ = 8x⁶y⁻³
8x⁶y⁻³4x³y
84reduce = 2
x³
y⁻⁴
2x³y⁴
Answer: 2x³y⁴
162reduce = 8
a⁻⁵b⁶
8b⁶a⁵
Answer: 8b⁶a⁵
x³y³ × y⁴x²
x¹y
xy
Answer: xy
p⁰ = 1
93reduce = 3
q⁶
3q⁶
Answer: 3q⁶
9x⁸ in the numerator, 81x² in the denominator.
981reduce = 19
x⁶9
Answer: x⁶9
Numerator: 12x²y
12x²y4y²
3x²y
Answer: 3x²y
xk−3 = x⁻²
k − 3 = −2
k = 1
Answer: k = 1
Move: a × ab² × b = a²b³
Quotient: a1−(−1)b-2−1 = a²b⁻³
Same result.
Answer: a²b³
Works: 10x³2x² = 5x.
Does not: 10x³2x⁴ = 5x.
Answer: e.g. 10x³ / 2x²
Need help simplifying exponent fractions?
Book a Session with Amy