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

This math topic focuses on the application of exponentiation rules, specifically solving equations involving powers and exponents. The problems entail finding a missing exponent (denoted as "?") when a base raised to a power (variable) is set equal to another base raised to an unknown power. Each question presents this challenge in increasingly complex forms, requiring the manipulation of exponents in reduced form, and applying the Power Law of exponents. Multiple choices are provided as potential answers, and learners must select the correct reduced form of the exponent based on the properties of exponents.

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

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Power Law - Exponent Base with Variable Power to Composite 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

(25)n=8?(2^{5})^{n} = 8^{?}

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

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Math worksheet on 'Exponents - Power Law - Exponent Base with Variable Power to Composite 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 4 ) to the power of n = 32 to the power of ?
a A LaTex expression showing ?=8n over 5
b A LaTex expression showing ?=6n
c A LaTex expression showing ?=4n over 8
d A LaTex expression showing ?=5n
e A LaTex expression showing ?=4n over 5
f A LaTex expression showing ?=15n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 5 ) to the power of n = 4 to the power of ?
a A LaTex expression showing ?=5n
b A LaTex expression showing ?=5n over 2
c A LaTex expression showing ?=4n
d A LaTex expression showing ?=7n
e A LaTex expression showing ?=2n
f A LaTex expression showing ?=10n over 2
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 4 ) to the power of n = 8 to the power of ?
a A LaTex expression showing ?=4n over 3
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=6n
d A LaTex expression showing ?=9n
e A LaTex expression showing ?=2 over 3n
f A LaTex expression showing ?=4n over 8
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of 2 ) to the power of n = 27 to the power of ?
a A LaTex expression showing ?=2n over 6
b A LaTex expression showing ?=3n over 3
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=9 over 2n
e A LaTex expression showing ?=5n
f A LaTex expression showing ?=2n over 3
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 3 ) to the power of n = 4 to the power of ?
a A LaTex expression showing ?=2 over 2n
b A LaTex expression showing ?=3n over 2
c A LaTex expression showing ?=3n over 9
d A LaTex expression showing ?=2n over 2
e A LaTex expression showing ?=8n
f A LaTex expression showing ?=6n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (4 to the power of 2 ) to the power of n = 64 to the power of ?
a A LaTex expression showing ?=2n over 3
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=4 over 3n
e A LaTex expression showing ?=2 over 4n
f A LaTex expression showing ?=6n over 2
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 2 ) to the power of n = 8 to the power of ?
a A LaTex expression showing ?=2n over 6
b A LaTex expression showing ?=4n
c A LaTex expression showing ?=2n over 3
d A LaTex expression showing ?=3n
e A LaTex expression showing ?=9n
f A LaTex expression showing ?=9n over 2