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

This math topic focuses on solving for unknown exponents based on the power law, specifically transitioning from a known exponent base with a variable power to an unknown exponent base with a known power. Each problem requires manipulating equations to isolate and determine the value of the missing exponent, considering base and exponent properties. The variations in the problems arise from different bases and powers, encouraging practice in simplifying expressions and deepening understanding of exponent rules in various contexts.

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 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

(24)n=(2?)8(2^{4})^{n} = (2^{?})^{8}

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

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Math worksheet on 'Exponents - Power Law - Exponent 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 (3 to the power of 3 ) to the power of n = (3 to the power of ? ) to the power of 9
a A LaTex expression showing ?=6n
b A LaTex expression showing ?=3 over 9n
c A LaTex expression showing ?=3n over 2
d A LaTex expression showing ?=n over 3
e A LaTex expression showing ?=6n over 3
f A LaTex expression showing ?=6 over 3n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 4 ) to the power of n = (2 to the power of ? ) to the power of 12
a A LaTex expression showing ?=9n
b A LaTex expression showing ?=6n
c A LaTex expression showing ?=9n over 4
d A LaTex expression showing ?=4n
e A LaTex expression showing ?=n over 3
f A LaTex expression showing ?=2n over 3
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of 4 ) to the power of n = (3 to the power of ? ) to the power of 8
a A LaTex expression showing ?=3n
b A LaTex expression showing ?=4n
c A LaTex expression showing ?=6n over 4
d A LaTex expression showing ?=3 over 3n
e A LaTex expression showing ?=n over 2
f A LaTex expression showing ?=4n over 8
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 2 ) to the power of n = (2 to the power of ? ) to the power of 4
a A LaTex expression showing ?=6n over 2
b A LaTex expression showing ?=2 over 3n
c A LaTex expression showing ?=n over 2
d A LaTex expression showing ?=2n over 3
e A LaTex expression showing ?=3n
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 3 ) to the power of n = (2 to the power of ? ) to the power of 9
a A LaTex expression showing ?=n over 3
b A LaTex expression showing ?=2 over 2n
c A LaTex expression showing ?=8n
d A LaTex expression showing ?=5n
e A LaTex expression showing ?=6 over 3n
f A LaTex expression showing ?=3n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 3 ) to the power of n = (2 to the power of ? ) to the power of 6
a A LaTex expression showing ?=5n
b A LaTex expression showing ?=2n over 5
c A LaTex expression showing ?=6n over 5
d A LaTex expression showing ?=n over 2
e A LaTex expression showing ?=10 over 3n
f A LaTex expression showing ?=10n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 4 ) to the power of n = (2 to the power of ? ) to the power of 8
a A LaTex expression showing ?=10n
b A LaTex expression showing ?=2n over 5
c A LaTex expression showing ?=n over 2
d A LaTex expression showing ?=2 over 5n
e A LaTex expression showing ?=4 over 8n
f A LaTex expression showing ?=5n