Algebra with Exponents - Binomial over Monomial and Constant

Level 1

This math topic focuses on solving algebraic expressions involving exponents, particularly binomials divided by monomials and constants. It tackles simplification and finding the value of a variable that satisfies the equation. The expressions include different powers such as squares and cubes. Each problem requires isolating the variable to determine its value, given the expression equated to a constant. For example, finding `n` when `6^( (n+12)/n) = 216` or `p` where `4^( (p+18)/p) = 64`. These problems are designed to enhance skills in manipulating and solving exponent-related algebraic equations.

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
A LaTex expression showing {{6}} to the power of {(\frac{{n + 12 }{{n}})}} = 216
Simplify and solve for n
a A LaTex expression showing n = 7
b A LaTex expression showing n = 6
2
A LaTex expression showing {{4}} to the power of {(\frac{{r + 18 }{{r}})}} = 16
Simplify and solve for r
a A LaTex expression showing r = 19
b A LaTex expression showing r = 18
3
A LaTex expression showing {{5}} to the power of {(\frac{{p + 12 }{{p}})}} = 125
Simplify and solve for p
a A LaTex expression showing p = 5
b A LaTex expression showing p = 6
4
A LaTex expression showing {{4}} to the power of {(\frac{{x + 8 }{{x}})}} = 64
Simplify and solve for x
a A LaTex expression showing x = 5
b A LaTex expression showing x = 4
5
A LaTex expression showing {{7}} to the power of {(\frac{{q + 45 }{{q}})}} = 49
Simplify and solve for q
a A LaTex expression showing q = 44
b A LaTex expression showing q = 45
6
A LaTex expression showing {{4}} to the power of {(\frac{{p + 18 }{{p}})}} = 64
Simplify and solve for p
a A LaTex expression showing p = 9
b A LaTex expression showing p = 10
7
A LaTex expression showing {{4}} to the power of {(\frac{{x + 72 }{{x}})}} = 16
Simplify and solve for x
a A LaTex expression showing x = 72
b A LaTex expression showing x = 71
8
A LaTex expression showing {{3}} to the power of {(\frac{{m + 64 }{{m}})}} = 9
Simplify and solve for m
a A LaTex expression showing m = 64
b A LaTex expression showing m = 66