Exponent

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

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

?

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 - Negative, Fractional, and Power Law' Learn online: app.mobius.academy/math/units/exponents_negatives_fractions_and_power_law/
1
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 ?=3n
b A LaTex expression showing ?=3 over 3n
c A LaTex expression showing ?=2 over 4n
d A LaTex expression showing ?=6n over 2
e A LaTex expression showing ?=2n over 3
f A LaTex expression showing ?=9n
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 ?=12n
b A LaTex expression showing ?=4 over 12n
c A LaTex expression showing ?=9 over 4n
d A LaTex expression showing ?=2n over 3
e A LaTex expression showing ?=4n over 3
f A LaTex expression showing ?=12n over 3
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 64 to the power of n = 16 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=3n over 6
d A LaTex expression showing ?=4 over 3n
e A LaTex expression showing ?=3n over 2
f A LaTex expression showing ?=3 over 6n
4
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 ?=3n over 6
b A LaTex expression showing ?=12n
c A LaTex expression showing ?=3n over 4
d A LaTex expression showing ?=3 over 6n
e A LaTex expression showing ?=3 over 4n
f A LaTex expression showing ?=8 over 3n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = 64 to the power of ?
a A LaTex expression showing ?=6 over 2n
b A LaTex expression showing ?=2n over 3
c A LaTex expression showing ?=6n over 2
d A LaTex expression showing ?=4n over 3
e A LaTex expression showing ?=6n
f A LaTex expression showing ?=9n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = 4 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=4 over 8n
c A LaTex expression showing ?=4n over 8
d A LaTex expression showing ?=6n
e A LaTex expression showing ?=4n
f A LaTex expression showing ?=2n over 2
7
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 ?=3 over 4n
b A LaTex expression showing ?=n over 2
c A LaTex expression showing ?=3n over 4
d A LaTex expression showing ?=5n
e A LaTex expression showing ?=12n
f A LaTex expression showing ?=2n