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

This math topic focuses on solving for unknown exponents by applying the power law of exponents. Specifically, it practices converting expressions with an exponent base raised to a variable power into an equivalent form with a prime base raised to an unknown power. Each question revolves around simplifying the given expression to identify the missing exponent value in reduced form, reinforcing understanding of exponent manipulation and reduction techniques.

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

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Power Law - Exponent Base with Variable Power to Prime 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

(25)n=2?(2^{5})^{n} = 2^{?}

Exponents - Power Law - Exponent Base with Variable Power to Prime Base with Unknown Power Worksheet

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Math worksheet on 'Exponents - Power Law - Exponent Base with Variable Power to Prime 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 2 ) to the power of n = 4 to the power of ?
a A LaTex expression showing ?=2n over 4
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=4n over 1
d A LaTex expression showing ?=2n
e A LaTex expression showing ?=6n
f A LaTex expression showing ?=n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 2 ) to the power of n = 2 to the power of ?
a A LaTex expression showing ?=3n over 2
b A LaTex expression showing ?=2n over 6
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=3n
e A LaTex expression showing ?=3 over 2n
f A LaTex expression showing ?=2n over 1
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of 4 ) to the power of n = 3 to the power of ?
a A LaTex expression showing ?=4n over 12
b A LaTex expression showing ?=7n
c A LaTex expression showing ?=3 over n
d A LaTex expression showing ?=12n over 1
e A LaTex expression showing ?=4 over 12n
f A LaTex expression showing ?=4n
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 4 ) to the power of n = 2 to the power of ?
a A LaTex expression showing ?=12n over 1
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=3 over 4n
d A LaTex expression showing ?=6n
e A LaTex expression showing ?=4 over 12n
f A LaTex expression showing ?=4n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of 3 ) to the power of n = 3 to the power of ?
a A LaTex expression showing ?=3 over 6n
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=6n over 1
d A LaTex expression showing ?=2n over 3
e A LaTex expression showing ?=n
f A LaTex expression showing ?=6n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 5 ) to the power of n = 2 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=2 over n
c A LaTex expression showing ?=7n
d A LaTex expression showing ?=n
e A LaTex expression showing ?=2n over 1
f A LaTex expression showing ?=5n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (5 to the power of 2 ) to the power of n = 5 to the power of ?
a A LaTex expression showing ?=2n over 2
b A LaTex expression showing ?=7n
c A LaTex expression showing ?=5n over 1
d A LaTex expression showing ?=2n
e A LaTex expression showing ?=5 over n
f A LaTex expression showing ?=4n over 1