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

This topic focuses on practicing the Power Law of exponents, specifically dealing with equations where both bases and exponents involve variables or calculations. The objective is to solve for missing exponents when given equations with composite bases and variable powers compared to an unknown exponent base with a known power. Multiple choice answers are provided, which require manipulation and simplification of exponential expressions to find the correct missing exponents in reduced form.

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 Unknown Exponent Base with Known 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

27n=(3?)927^{n} = (3^{?})^{9}

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

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Math worksheet on 'Exponents - Power Law - Composite Base with Variable Power to Unknown Exponent Base with Known 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 16 to the power of n = (2 to the power of ? ) to the power of 8
a A LaTex expression showing ?=4n over 4
b A LaTex expression showing ?=4n
c A LaTex expression showing ?=n over 2
d A LaTex expression showing ?=6n
e A LaTex expression showing ?=4 over 4n
f A LaTex expression showing ?=2n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 8 to the power of n = (2 to the power of ? ) to the power of 6
a A LaTex expression showing ?=5n
b A LaTex expression showing ?=2n
c A LaTex expression showing ?=3 over 6n
d A LaTex expression showing ?=n over 2
e A LaTex expression showing ?=2 over 2n
f A LaTex expression showing ?=3n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 27 to the power of n = (3 to the power of ? ) to the power of 9
a A LaTex expression showing ?=n over 3
b A LaTex expression showing ?=6n over 3
c A LaTex expression showing ?=3n over 9
d A LaTex expression showing ?=2n
e A LaTex expression showing ?=3 over 9n
f A LaTex expression showing ?=9n over 2
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = (2 to the power of ? ) to the power of 6
a A LaTex expression showing ?=12 over 2n
b A LaTex expression showing ?=2n over 4
c A LaTex expression showing ?=n over 3
d A LaTex expression showing ?=2 over 6n
e A LaTex expression showing ?=16n
f A LaTex expression showing ?=4n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = (2 to the power of ? ) to the power of 12
a A LaTex expression showing ?=2n over 3
b A LaTex expression showing ?=n over 3
c A LaTex expression showing ?=12n over 3
d A LaTex expression showing ?=9n over 4
e A LaTex expression showing ?=9n
f A LaTex expression showing ?=2 over 3n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = (4 to the power of ? ) to the power of 4
a A LaTex expression showing ?=6n
b A LaTex expression showing ?=6n over 2
c A LaTex expression showing ?=4 over 3n
d A LaTex expression showing ?=2n
e A LaTex expression showing ?=9n
f A LaTex expression showing ?=n over 2
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 64 to the power of n = (4 to the power of ? ) to the power of 6
a A LaTex expression showing ?=7n
b A LaTex expression showing ?=n over 2
c A LaTex expression showing ?=4n
d A LaTex expression showing ?=4 over 3n
e A LaTex expression showing ?=4 over 2n
f A LaTex expression showing ?=3 over 6n