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

This math topic focuses on solving for unknown exponents within equations that involve bases raised to variable or fixed powers. The problems involve solving expressions where both sides contain powers of composite numbers. Students are expected to manipulate equations using the power law to isolate and solve for the unknown exponent, presented in multiple-choice format with various potential solutions for each problem. This is part of a broader introduction to exponents and power laws.

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

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Power Law - Composite Base with Variable 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

16n=4?16^{n} = 4^{?}

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

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Math worksheet on 'Exponents - Power Law - Composite Base with Variable 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 4 to the power of n = 32 to the power of ?
a A LaTex expression showing ?=10 over 2n
b A LaTex expression showing ?=4n over 5
c A LaTex expression showing ?=5n
d A LaTex expression showing ?=2n over 5
e A LaTex expression showing ?=10n
f A LaTex expression showing ?=10n over 2
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = 8 to the power of ?
a A LaTex expression showing ?=4n over 3
b A LaTex expression showing ?=4 over 12n
c A LaTex expression showing ?=12n
d A LaTex expression showing ?=2n over 3
e A LaTex expression showing ?=12n over 3
f A LaTex expression showing ?=9 over 4n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 9 to the power of n = 27 to the power of ?
a A LaTex expression showing ?=2n over 3
b A LaTex expression showing ?=6n over 2
c A LaTex expression showing ?=2 over 4n
d A LaTex expression showing ?=9n
e A LaTex expression showing ?=3n
f A LaTex expression showing ?=3 over 3n
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 9 to the power of n = 81 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=5n
c A LaTex expression showing ?=12n
d A LaTex expression showing ?=n over 2
e A LaTex expression showing ?=3 over 4n
f A LaTex expression showing ?=3n over 4
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 32 to the power of n = 16 to the power of ?
a A LaTex expression showing ?=7n
b A LaTex expression showing ?=5n
c A LaTex expression showing ?=5 over 15n
d A LaTex expression showing ?=12 over 5n
e A LaTex expression showing ?=5n over 4
f A LaTex expression showing ?=15n over 4
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = 8 to the power of ?
a A LaTex expression showing ?=2n over 4
b A LaTex expression showing ?=2 over 4n
c A LaTex expression showing ?=3n
d A LaTex expression showing ?=2n over 3
e A LaTex expression showing ?=6n
f A LaTex expression showing ?=4n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 27 to the power of n = 81 to the power of ?
a A LaTex expression showing ?=3 over 9n
b A LaTex expression showing ?=12n over 3
c A LaTex expression showing ?=3n over 4
d A LaTex expression showing ?=12 over 3n
e A LaTex expression showing ?=3n over 9
f A LaTex expression showing ?=16n