Algebra with Exponents - Binomial over Binomial and Constant

Level 2

This math topic focuses on simplifying and solving algebraic expressions involving exponents, with a specific focus on binomial ratios raised to a power. Each problem presents an equation where a constant is raised to the power of a fraction, involving linear expressions of a variable in both the numerator and denominator. The goal is to solve for the variable, with multiple choice answers provided for each question. The skills practiced include manipulating powers and exponents, particularly negative and fractional exponents, and solving for a variable within these contexts.

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

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Algebra with Exponents - Binomial over Binomial and Constant Worksheet

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Algebra with Exponents - Binomial over Binomial and Constant
1
Simplify and solve for y
A LaTex expression showing {{2}} to the power of {(\frac{{7y - 9 }{{4y - 8}})}} = 8
a A LaTex expression showing y = 5
b A LaTex expression showing y = 3
c A LaTex expression showing y = 4
d A LaTex expression showing y = 2
2
Simplify and solve for t
A LaTex expression showing {{5}} to the power of {(\frac{{5t + 6 }{{3t - 4}})}} = 25
a A LaTex expression showing t = 14
b A LaTex expression showing t = 16
c A LaTex expression showing t = 15
d A LaTex expression showing t = 13
3
Simplify and solve for m
A LaTex expression showing {{2}} to the power of {(\frac{{3m - 8 }{{9m - 2}})}} = 16
a A LaTex expression showing m = 0
b A LaTex expression showing m = 2
c A LaTex expression showing m = 1
d A LaTex expression showing m = -1
4
Simplify and solve for y
A LaTex expression showing {{3}} to the power of {(\frac{{4y + 8 }{{8y - 2}})}} = 9
a A LaTex expression showing y = 0
b A LaTex expression showing y = 3
c A LaTex expression showing y = 2
d A LaTex expression showing y = 1
5
Simplify and solve for m
A LaTex expression showing {{5}} to the power of {(\frac{{7m + 9 }{{2m - 3}})}} = 25
a A LaTex expression showing m = -5
b A LaTex expression showing m = -4
c A LaTex expression showing m = -3
d A LaTex expression showing m = -6
6
Simplify and solve for p
A LaTex expression showing {{2}} to the power of {(\frac{{5p + 7 }{{8p - 5}})}} = 16
a A LaTex expression showing p = 0
b A LaTex expression showing p = 1
c A LaTex expression showing p = 3
d A LaTex expression showing p = 2
7
Simplify and solve for x
A LaTex expression showing {{4}} to the power of {(\frac{{7x - 6 }{{4x - 9}})}} = 16
a A LaTex expression showing x = 11
b A LaTex expression showing x = 14
c A LaTex expression showing x = 13
d A LaTex expression showing x = 12
8
Simplify and solve for q
A LaTex expression showing {{3}} to the power of {(\frac{{7q - 4 }{{5q - 8}})}} = 9
a A LaTex expression showing q = 4
b A LaTex expression showing q = 3
c A LaTex expression showing q = 6
d A LaTex expression showing q = 5