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

This math topic focuses on solving for unknown exponents in equations involving prime bases raised to variable powers, which themselves are raised to fixed powers. Each problem presents an equation where students are asked to find the correct expression for the missing exponent in its reduced form. The provided equations challenge students to apply their understanding of the properties of exponents, particularly the power of a power rule, to simplify and solve for the unknown values effectively. The problems increase in complexity, offering several potential answers to select from, enhancing skill in both exponent rules and algebraic manipulation.

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

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Power Law - Prime 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

2n=(2?)22^{n} = (2^{?})^{2}

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

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Math worksheet on 'Exponents - Power Law - Prime 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 2 to the power of n = (2 to the power of ? ) to the power of 2
a A LaTex expression showing ?=6n
b A LaTex expression showing ?=n
c A LaTex expression showing ?=1 over 2n
d A LaTex expression showing ?=6 over n
e A LaTex expression showing ?=9n
f A LaTex expression showing ?=n over 2
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = (4 to the power of ? ) to the power of 2
a A LaTex expression showing ?=1 over 2n
b A LaTex expression showing ?=n
c A LaTex expression showing ?=n over 2
d A LaTex expression showing ?=4 over n
e A LaTex expression showing ?=4n over 2
f A LaTex expression showing ?=2n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = (4 to the power of ? ) to the power of 3
a A LaTex expression showing ?=3n over 2
b A LaTex expression showing ?=n over 3
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=4n over 2
e A LaTex expression showing ?=8n
f A LaTex expression showing ?=6 over n
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 3 to the power of n = (3 to the power of ? ) to the power of 2
a A LaTex expression showing ?=n
b A LaTex expression showing ?=1 over 2n
c A LaTex expression showing ?=12n
d A LaTex expression showing ?=4n
e A LaTex expression showing ?=n over 2
f A LaTex expression showing ?=2n over 4
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 2 to the power of n = (2 to the power of ? ) to the power of 3
a A LaTex expression showing ?=3n
b A LaTex expression showing ?=8n
c A LaTex expression showing ?=3n over 2
d A LaTex expression showing ?=n
e A LaTex expression showing ?=2 over 2n
f A LaTex expression showing ?=n over 3
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 6 to the power of n = (6 to the power of ? ) to the power of 2
a A LaTex expression showing ?=6n over 2
b A LaTex expression showing ?=n over 2
c A LaTex expression showing ?=n
d A LaTex expression showing ?=1 over 2n
e A LaTex expression showing ?=4n
f A LaTex expression showing ?=6 over 2n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 3 to the power of n = (3 to the power of ? ) to the power of 3
a A LaTex expression showing ?=3n over 4
b A LaTex expression showing ?=3 over 4n
c A LaTex expression showing ?=12n over 1
d A LaTex expression showing ?=12n
e A LaTex expression showing ?=12 over n
f A LaTex expression showing ?=n over 3