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

This math topic focuses on solving for unknown exponents in equations involving powers, primarily working with expressions converting composite bases with variable exponents to prime bases. The problems require reducing the resultant exponents to simpler forms and selecting the correct answer from multiple choices. This requires understanding and application of powers and laws of exponents, essential skills for algebraic manipulation in higher mathematics. Each problem is presented with a mathematical expression and multiple potential answers, reinforcing exponent manipulation skills in a progressive manner.

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

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Power Law - Composite Base with Variable Power to Prime 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

27n=3?27^{n} = 3^{?}

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

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Math worksheet on 'Exponents - Power Law - Composite Base with Variable Power to Prime 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 25 to the power of n = 5 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=5 over n
c A LaTex expression showing ?=7n
d A LaTex expression showing ?=5n over 1
e A LaTex expression showing ?=2 over 2n
f A LaTex expression showing ?=4n over 1
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = 2 to the power of ?
a A LaTex expression showing ?=6n
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=2n over 1
d A LaTex expression showing ?=4n
e A LaTex expression showing ?=2 over n
f A LaTex expression showing ?=8n over 1
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 81 to the power of n = 3 to the power of ?
a A LaTex expression showing ?=3n over 1
b A LaTex expression showing ?=4 over 12n
c A LaTex expression showing ?=3n
d A LaTex expression showing ?=3 over n
e A LaTex expression showing ?=7n
f A LaTex expression showing ?=4n
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 64 to the power of n = 4 to the power of ?
a A LaTex expression showing ?=3n
b A LaTex expression showing ?=2 over 3n
c A LaTex expression showing ?=3n over 6
d A LaTex expression showing ?=6n over 1
e A LaTex expression showing ?=n
f A LaTex expression showing ?=7n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 36 to the power of n = 6 to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=2n over 2
c A LaTex expression showing ?=2n over 4
d A LaTex expression showing ?=2 over 4n
e A LaTex expression showing ?=6n over 1
f A LaTex expression showing ?=2 over 2n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = 2 to the power of ?
a A LaTex expression showing ?=4n
b A LaTex expression showing ?=2n over 4
c A LaTex expression showing ?=2n over 1
d A LaTex expression showing ?=3n
e A LaTex expression showing ?=2 over n
f A LaTex expression showing ?=2n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = 4 to the power of ?
a A LaTex expression showing ?=4n over 1
b A LaTex expression showing ?=2 over 6n
c A LaTex expression showing ?=6n over 1
d A LaTex expression showing ?=4n
e A LaTex expression showing ?=3n over 2
f A LaTex expression showing ?=2n