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

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Exponents - Power Law - Exponent Base with Variable Power to Prime Base with Unknown Power
1
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (2 to the power of 5 ) to the power of n = 2 to the power of x
a A LaTex expression showing x=3n over 5
b A LaTex expression showing x=4n
c A LaTex expression showing x=5n over 15
d A LaTex expression showing x=n
e A LaTex expression showing x=5n
f A LaTex expression showing x=2 over n
2
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (3 to the power of 4 ) to the power of n = 3 to the power of x
a A LaTex expression showing x=4n
b A LaTex expression showing x=3 over n
c A LaTex expression showing x=7n
d A LaTex expression showing x=n
e A LaTex expression showing x=3n
f A LaTex expression showing x=4 over 8n
3
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (5 to the power of 2 ) to the power of n = 5 to the power of x
a A LaTex expression showing x=2n over 4
b A LaTex expression showing x=2n
c A LaTex expression showing x=3n
d A LaTex expression showing x=7n
e A LaTex expression showing x=n
f A LaTex expression showing x=5 over n
4
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (4 to the power of 3 ) to the power of n = 4 to the power of x
a A LaTex expression showing x=3n over 9
b A LaTex expression showing x=3n
c A LaTex expression showing x=7n
d A LaTex expression showing x=4n
e A LaTex expression showing x=n
f A LaTex expression showing x=3 over 9n
5
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (2 to the power of 4 ) to the power of n = 2 to the power of x
a A LaTex expression showing x=4n
b A LaTex expression showing x=n
c A LaTex expression showing x=2n over 1
d A LaTex expression showing x=4 over 8n
e A LaTex expression showing x=3n
f A LaTex expression showing x=8n over 1
6
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (2 to the power of 3 ) to the power of n = 2 to the power of x
a A LaTex expression showing x=5n
b A LaTex expression showing x=3n
c A LaTex expression showing x=2n over 1
d A LaTex expression showing x=n
e A LaTex expression showing x=2n over 3
f A LaTex expression showing x=6n over 1
7
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (3 to the power of 3 ) to the power of n = 3 to the power of x
a A LaTex expression showing x=3 over 6n
b A LaTex expression showing x=3n over 1
c A LaTex expression showing x=3n over 6
d A LaTex expression showing x=3 over n
e A LaTex expression showing x=6n
f A LaTex expression showing x=3n
8
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (3 to the power of 2 ) to the power of n = 3 to the power of x
a A LaTex expression showing x=2n over 2
b A LaTex expression showing x=5n
c A LaTex expression showing x=n
d A LaTex expression showing x=3n over 1
e A LaTex expression showing x=2 over 2n
f A LaTex expression showing x=2n