Algebra with Exponents - Binomial over Constant and Monomial

Level 2

This topic focuses on practicing algebra involving exponents, particularly those that include binomials divided by constants and monomials. It delves into simplifying and solving exponential equations to find the variable's value. The problems require manipulating expressions with negative, fractional, and power law exponents, involving comparisons of exponential terms to solve for variables such as "x," "q," "r," "t," and "w." Each question includes multiple-choice answers to test comprehension and application of the exponent rules in various contexts.

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

more

Algebra with Exponents - Binomial over Constant and Monomial Worksheet

Mobius Math Academy logo
Algebra with Exponents - Binomial over Constant and Monomial
1
Simplify and solve for x
A LaTex expression showing {{7}} to the power of {(\frac{{2x + 8 }{{5}})}} = 49 to the power of x
a A LaTex expression showing x = 1
b A LaTex expression showing x = 0
c A LaTex expression showing x = 2
d A LaTex expression showing x = 3
2
Simplify and solve for x
A LaTex expression showing {{6}} to the power of {(\frac{{5x + 3 }{{2}})}} = 36 to the power of x
a A LaTex expression showing x = -2
b A LaTex expression showing x = -4
c A LaTex expression showing x = -1
d A LaTex expression showing x = -3
3
Simplify and solve for q
A LaTex expression showing {{3}} to the power of {(\frac{{9q + 5 }{{4}})}} = 9 to the power of q
a A LaTex expression showing q = -4
b A LaTex expression showing q = -5
c A LaTex expression showing q = -3
d A LaTex expression showing q = -6
4
Simplify and solve for r
A LaTex expression showing {{8}} to the power of {(\frac{{3r + 9 }{{3}})}} = 64 to the power of r
a A LaTex expression showing r = 3
b A LaTex expression showing r = 2
c A LaTex expression showing r = 4
d A LaTex expression showing r = 5
5
Simplify and solve for t
A LaTex expression showing {{3}} to the power of {(\frac{{7t - 5 }{{3}})}} = 81 to the power of t
a A LaTex expression showing t = -2
b A LaTex expression showing t = 0
c A LaTex expression showing t = 1
d A LaTex expression showing t = -1
6
Simplify and solve for w
A LaTex expression showing {{4}} to the power of {(\frac{{6w - 8 }{{4}})}} = 16 to the power of w
a A LaTex expression showing w = -2
b A LaTex expression showing w = -3
c A LaTex expression showing w = -5
d A LaTex expression showing w = -4
7
Simplify and solve for r
A LaTex expression showing {{4}} to the power of {(\frac{{7r + 8 }{{3}})}} = 16 to the power of r
a A LaTex expression showing r = -6
b A LaTex expression showing r = -9
c A LaTex expression showing r = -8
d A LaTex expression showing r = -7
8
Simplify and solve for r
A LaTex expression showing {{9}} to the power of {(\frac{{8r + 4 }{{3}})}} = 81 to the power of r
a A LaTex expression showing r = -2
b A LaTex expression showing r = -3
c A LaTex expression showing r = -1
d A LaTex expression showing r = 0