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

This math topic focuses on applying the power law of exponents across various problems. It deals primarily with solving for unknown exponents when given equations involving prime bases raised to variable powers and exponent bases. These problems require understanding and manipulating exponential forms to deduce the missing exponents in their simplest, reduced form. The set includes examples with numerical and variable bases, developing skills in algebraic manipulation related to exponents. The context for these practice problems is part of an introductory unit on the power laws of exponents.

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 Exponent 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

3n=(32)?3^{n} = (3^{2})^{?}

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

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