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Exponents

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

This math topic focuses on solving equations using the power law in exponents. Specifically, students practice finding an unknown exponent in expressions where both the exponent base and the powers are variable but partially known. Each problem presents an equation involving exponents, requiring the student to solve for the missing exponent in reduced form, applying their understanding of properties of exponents and algebraic manipulation skills.

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

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

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Exponents - Power Law - Variable Exponent Base with Known Power to Unknown Exponent Base with Known Power
1
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 15 = (2 to the power of x ) to the power of 9
a A LaTex expression showing x=15n
b A LaTex expression showing x=5n over 3
c A LaTex expression showing x=3 over 9n
d A LaTex expression showing x=15n over 3
e A LaTex expression showing x=5n
f A LaTex expression showing x=3n
2
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 10 = (2 to the power of x ) to the power of 6
a A LaTex expression showing x=3n
b A LaTex expression showing x=5n over 3
c A LaTex expression showing x=10n
d A LaTex expression showing x=6n over 5
e A LaTex expression showing x=10 over 3n
f A LaTex expression showing x=3 over 6n
3
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (4 to the power of n ) to the power of 4 = (4 to the power of x ) to the power of 6
a A LaTex expression showing x=6n
b A LaTex expression showing x=2n
c A LaTex expression showing x=3n over 6
d A LaTex expression showing x=4n over 2
e A LaTex expression showing x=3n
f A LaTex expression showing x=2n over 3
4
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (4 to the power of n ) to the power of 9 = (4 to the power of x ) to the power of 6
a A LaTex expression showing x=2n
b A LaTex expression showing x=3n
c A LaTex expression showing x=12n
d A LaTex expression showing x=3n over 2
e A LaTex expression showing x=4n over 3
f A LaTex expression showing x=6n over 3
5
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 6 = (3 to the power of x ) to the power of 4
a A LaTex expression showing x=9n
b A LaTex expression showing x=3 over 3n
c A LaTex expression showing x=3n over 3
d A LaTex expression showing x=3n over 2
e A LaTex expression showing x=4n over 3
f A LaTex expression showing x=5n
6
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 4 = (2 to the power of x ) to the power of 6
a A LaTex expression showing x=3n over 6
b A LaTex expression showing x=2n over 3
c A LaTex expression showing x=2 over 2n
d A LaTex expression showing x=2n over 2
e A LaTex expression showing x=6n
f A LaTex expression showing x=4n over 3
7
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (4 to the power of n ) to the power of 6 = (4 to the power of x ) to the power of 9
a A LaTex expression showing x=6n over 3
b A LaTex expression showing x=2n over 3
c A LaTex expression showing x=3n
d A LaTex expression showing x=8n
e A LaTex expression showing x=2n
f A LaTex expression showing x=7n
8
Solve for the missing exponent (x) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 12 = (3 to the power of x ) to the power of 6
a A LaTex expression showing x=2n over 6
b A LaTex expression showing x=2n
c A LaTex expression showing x=6n over 4
d A LaTex expression showing x=5n
e A LaTex expression showing x=16n
f A LaTex expression showing x=4n