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Exponents - Power Law - Variable Exponent Base with Known Power to Composite Base with Unknown Power (Level 1)

This math topic focuses on solving for missing exponents in expressions where bases and some exponents are variables or known values. Problems involve manipulating expressions using the power law of exponents, which help in solving for unknown exponents when equalities are given. Each question requires reducing the result to its simplest form. This topic is a part of an introductory unit on power laws of exponents, aiming to strengthen understanding of basic exponentiation rules and their applications.

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

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Power Law - Variable Exponent Base with Known Power to Composite Base with Unknown Power

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Solve for the missing exponent (?) in reduced form

(3n)12=81?(3^{n})^{12} = 81^{?}

Exponents - Power Law - Variable Exponent Base with Known Power to Composite Base with Unknown Power Worksheet

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Math worksheet on 'Exponents - Power Law - Variable Exponent Base with Known Power to Composite Base with Unknown Power (Level 1)'. Part of a broader unit on 'Exponents - Multiplication and Division - Advanced' Learn online: app.mobius.academy/math/units/exponents_multiplication_and_division_advanced/
1
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 4 = 9 to the power of ?
a A LaTex expression showing ?=3 over 2n
b A LaTex expression showing ?=6n
c A LaTex expression showing ?=4n over 4
d A LaTex expression showing ?=8n over 2
e A LaTex expression showing ?=2n
f A LaTex expression showing ?=4 over 8n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 6 = 9 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=8n
c A LaTex expression showing ?=3n
d A LaTex expression showing ?=6 over 3n
e A LaTex expression showing ?=3n over 2
f A LaTex expression showing ?=6n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 4 = 4 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=4n
c A LaTex expression showing ?=6n
d A LaTex expression showing ?=5n over 10
e A LaTex expression showing ?=7n
f A LaTex expression showing ?=2n over 2
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 8 = 16 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=5 over 10n
c A LaTex expression showing ?=8n over 5
d A LaTex expression showing ?=10n over 4
e A LaTex expression showing ?=7n
f A LaTex expression showing ?=5n over 10
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 8 = 81 to the power of ?
a A LaTex expression showing ?=8n
b A LaTex expression showing ?=2 over 4n
c A LaTex expression showing ?=2n over 4
d A LaTex expression showing ?=8 over 2n
e A LaTex expression showing ?=5n
f A LaTex expression showing ?=2n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 12 = 81 to the power of ?
a A LaTex expression showing ?=12n
b A LaTex expression showing ?=12n over 2
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=3 over 4n
e A LaTex expression showing ?=2 over 6n
f A LaTex expression showing ?=3n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (4 to the power of n ) to the power of 6 = 16 to the power of ?
a A LaTex expression showing ?=9n over 2
b A LaTex expression showing ?=4 over 2n
c A LaTex expression showing ?=7n
d A LaTex expression showing ?=8n
e A LaTex expression showing ?=3n over 9
f A LaTex expression showing ?=3n