Algebra with Exponents - Binomial over Constant and Monomial

Level 1

This math topic focuses on manipulating algebraic expressions that involve exponents, specifically solving equations with binomials raised to fractional powers set equal to monomials raised to variable powers. It's part of a broader study on negative, fractional, and power laws of exponents. The problems in this topic require learners to simplify and solve for a variable, aiding in the development of their skills in handling complex exponent rules and fostering algebraic thinking. The questions are designed to test the understanding of exponent manipulation and variable isolation in different scenarios.

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

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Algebra with Exponents - Binomial over Constant and Monomial Worksheet

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Algebra with Exponents - Binomial over Constant and Monomial
1
A LaTex expression showing {{7}} to the power of {(\frac{{y + 9 }{{5}})}} = 49 to the power of y
Simplify and solve for y
a A LaTex expression showing y = 1
b A LaTex expression showing y = 3
2
A LaTex expression showing {{6}} to the power of {(\frac{{z + 9 }{{5}})}} = 36 to the power of z
Simplify and solve for z
a A LaTex expression showing z = 1
b A LaTex expression showing z = 3
3
A LaTex expression showing {{6}} to the power of {(\frac{{n + 9 }{{5}})}} = 36 to the power of n
Simplify and solve for n
a A LaTex expression showing n = 1
b A LaTex expression showing n = 2
4
A LaTex expression showing {{5}} to the power of {(\frac{{m + 6 }{{2}})}} = 25 to the power of m
Simplify and solve for m
a A LaTex expression showing m = 3
b A LaTex expression showing m = 2
5
A LaTex expression showing {{7}} to the power of {(\frac{{r + 9 }{{2}})}} = 49 to the power of r
Simplify and solve for r
a A LaTex expression showing r = 5
b A LaTex expression showing r = 3
6
A LaTex expression showing {{8}} to the power of {(\frac{{t + 7 }{{4}})}} = 64 to the power of t
Simplify and solve for t
a A LaTex expression showing t = 0
b A LaTex expression showing t = 1
7
A LaTex expression showing {{4}} to the power of {(\frac{{p - 9 }{{2}})}} = 16 to the power of p
Simplify and solve for p
a A LaTex expression showing p = -3
b A LaTex expression showing p = -2
8
A LaTex expression showing {{8}} to the power of {(\frac{{n + 9 }{{2}})}} = 64 to the power of n
Simplify and solve for n
a A LaTex expression showing n = 3
b A LaTex expression showing n = 5