Algebra with Exponents - Binomial over Monomial and Constant

Level 2

This math topic focuses on simplifying expressions involving exponents, particularly with binomials divided by monomials and constants. The problems involve solving for a variable (m, x, n, z) where the variable is part of the exponent in a power equation. The exponents are represented in fractional forms, and the equations compare the exponents of bases (like 3, 6, 7, and 8) to specific numbers. Each question presents multiple choices for the solution, testing understanding of the power law, handling fractional or negative exponents, and the ability to manipulate algebraic expressions to isolate and solve for variables.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Algebra with Exponents - Binomial over Monomial and Constant Worksheet

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Algebra with Exponents - Binomial over Monomial and Constant
1
Simplify and solve for m
A LaTex expression showing {{3}} to the power of {(\frac{{5m + 63 }{{7m }})}} = 9
a A LaTex expression showing m = 8
b A LaTex expression showing m = 7
c A LaTex expression showing m = 6
d A LaTex expression showing m = 9
2
Simplify and solve for x
A LaTex expression showing {{7}} to the power of {(\frac{{5x + 18 }{{2x }})}} = 49
a A LaTex expression showing x = -19
b A LaTex expression showing x = -18
c A LaTex expression showing x = -17
d A LaTex expression showing x = -16
3
Simplify and solve for n
A LaTex expression showing {{8}} to the power of {(\frac{{7n + 27 }{{5n }})}} = 64
a A LaTex expression showing n = 10
b A LaTex expression showing n = 8
c A LaTex expression showing n = 9
d A LaTex expression showing n = 11
4
Simplify and solve for m
A LaTex expression showing {{6}} to the power of {(\frac{{4m + 56 }{{6m }})}} = 216
a A LaTex expression showing m = 4
b A LaTex expression showing m = 5
c A LaTex expression showing m = 3
d A LaTex expression showing m = 6
5
Simplify and solve for z
A LaTex expression showing {{3}} to the power of {(\frac{{9z + 20 }{{4z }})}} = 9
a A LaTex expression showing z = -19
b A LaTex expression showing z = -18
c A LaTex expression showing z = -21
d A LaTex expression showing z = -20
6
Simplify and solve for z
A LaTex expression showing {{6}} to the power of {(\frac{{9z + 18 }{{4z }})}} = 216
a A LaTex expression showing z = 7
b A LaTex expression showing z = 6
c A LaTex expression showing z = 8
d A LaTex expression showing z = 5
7
Simplify and solve for x
A LaTex expression showing {{3}} to the power of {(\frac{{2x + 36 }{{5x }})}} = 81
a A LaTex expression showing x = 2
b A LaTex expression showing x = 4
c A LaTex expression showing x = 3
d A LaTex expression showing x = 1
8
Simplify and solve for z
A LaTex expression showing {{4}} to the power of {(\frac{{7z + 36 }{{4z }})}} = 16
a A LaTex expression showing z = 37
b A LaTex expression showing z = 35
c A LaTex expression showing z = 38
d A LaTex expression showing z = 36