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

This math topic focuses on applying the power law of exponents to solve for unknown powers. Students utilize algebraic methods to determine the exponent in equations where bases with variable and unknown powers are equated. Problems include converting expressions with multiple levels of exponentiation into their simplest forms and solving for the missing exponent values. The exercises involve recognizing and manipulating bases and their powers to establish equivalence between the two sides of an equation, enhancing students' algebraic proficiency and understanding of exponent rules.

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 Exponent Base with Unknown Power Worksheet

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