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

This math topic focuses on practicing the power law of exponents, specifically solving for unknown powers when the base and other parts of the exponent are known. Using base 10, the problems involve simplifying expressions where an exponent is applied to another exponent, equating them to another power form, and then solving for a missing exponent value. This helps strengthen understanding of exponent manipulation including multiplication rules for exponents. This is part of a broader unit on exponents that includes negative, fractional, and various power laws.

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 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 (?)

(103)4=(102)?(10^{3})^{4} = (10^{2})^{?}

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

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Math worksheet on 'Exponents - Power Law - Exponent Base with Variable Power to Exponent Base with Unknown Power (Level 1)'. Part of a broader unit on 'Exponents - Power Law - Practice' Learn online: app.mobius.academy/math/units/exponents_power_law_practice/
1
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 8 = (10 to the power of 4 ) to the power of ?
a A LaTex expression showing ?=6
b A LaTex expression showing ?=5
c A LaTex expression showing ?=1
d A LaTex expression showing ?=4
e A LaTex expression showing ?=9
f A LaTex expression showing ?=3
2
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 12 = (10 to the power of 4 ) to the power of ?
a A LaTex expression showing ?=1
b A LaTex expression showing ?=5
c A LaTex expression showing ?=13
d A LaTex expression showing ?=4
e A LaTex expression showing ?=6
f A LaTex expression showing ?=14
3
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 6 = (10 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=15
b A LaTex expression showing ?=2
c A LaTex expression showing ?=11
d A LaTex expression showing ?=9
e A LaTex expression showing ?=5
f A LaTex expression showing ?=3
4
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 4 ) to the power of 4 = (10 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=13
b A LaTex expression showing ?=2
c A LaTex expression showing ?=8
d A LaTex expression showing ?=12
e A LaTex expression showing ?=11
f A LaTex expression showing ?=9
5
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 12 = (10 to the power of 4 ) to the power of ?
a A LaTex expression showing ?=1
b A LaTex expression showing ?=16
c A LaTex expression showing ?=4
d A LaTex expression showing ?=2
e A LaTex expression showing ?=9
f A LaTex expression showing ?=8
6
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 4 ) to the power of 6 = (10 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=8
b A LaTex expression showing ?=1
c A LaTex expression showing ?=9
d A LaTex expression showing ?=11
e A LaTex expression showing ?=2
f A LaTex expression showing ?=3
7
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 9 = (10 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=9
b A LaTex expression showing ?=13
c A LaTex expression showing ?=10
d A LaTex expression showing ?=11
e A LaTex expression showing ?=3
f A LaTex expression showing ?=6