Algebra with Exponents - Binomial and Constant

Level 2

This math topic focuses on solving algebraic equations involving exponents, specifically with binomials and constants. It is part of a larger unit on negative, fractional, and power laws of exponents. The exercises require simplifying exponential expressions and solving for variables, such as x, p, t, w, and y, in equations like \(2^{(6x - 9)} = 8\) and \(3^{(6p + 8)} = 9\). Each question provides multiple-choice answers, requiring understanding of exponent properties to identify the correct value of the variable.

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

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Algebra with Exponents - Binomial and Constant Worksheet

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Algebra with Exponents - Binomial and Constant
1
Simplify and solve for x
A LaTex expression showing {{2}} to the power of {(6x - 9) } = 8
a A LaTex expression showing x = 3
b A LaTex expression showing x = 4
c A LaTex expression showing x = 1
d A LaTex expression showing x = 2
2
Simplify and solve for p
A LaTex expression showing {{3}} to the power of {(6p + 8) } = 9
a A LaTex expression showing p = 1
b A LaTex expression showing p = -2
c A LaTex expression showing p = -1
d A LaTex expression showing p = 0
3
Simplify and solve for t
A LaTex expression showing {{6}} to the power of {(2t - 4) } = 36
a A LaTex expression showing t = 4
b A LaTex expression showing t = 3
c A LaTex expression showing t = 5
d A LaTex expression showing t = 2
4
Simplify and solve for w
A LaTex expression showing {{6}} to the power of {(5w + 7) } = 36
a A LaTex expression showing w = 0
b A LaTex expression showing w = -2
c A LaTex expression showing w = 1
d A LaTex expression showing w = -1
5
Simplify and solve for y
A LaTex expression showing {{3}} to the power of {(5y - 8) } = 9
a A LaTex expression showing y = 2
b A LaTex expression showing y = 3
c A LaTex expression showing y = 1
d A LaTex expression showing y = 4
6
Simplify and solve for y
A LaTex expression showing {{2}} to the power of {(7y - 4) } = 8
a A LaTex expression showing y = 2
b A LaTex expression showing y = 1
c A LaTex expression showing y = 0
d A LaTex expression showing y = 3
7
Simplify and solve for y
A LaTex expression showing {{4}} to the power of {(5y + 7) } = 16
a A LaTex expression showing y = -2
b A LaTex expression showing y = 1
c A LaTex expression showing y = -1
d A LaTex expression showing y = 0
8
Simplify and solve for x
A LaTex expression showing {{8}} to the power of {(2x + 6) } = 64
a A LaTex expression showing x = 0
b A LaTex expression showing x = -2
c A LaTex expression showing x = -3
d A LaTex expression showing x = -1