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

This math topic focuses on solving problems involving exponents, specifically using the power law. It centers on finding the missing exponent when base ten is raised to the power of another exponent. Problems include expressions like \( (10^2)^3 = 10^? \), testing the ability to apply the rule that states \( (a^m)^n = a^{m \cdot n} \). Each question requires the student to determine the correct power of ten that equates to the given expression, honing skills in exponentiation and understanding of power laws. The problems are presented at a beginner level.

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 Ten 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 (?)

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

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

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Math worksheet on 'Exponents - Power Law - Exponent Base with Variable Power to Ten 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 4 ) to the power of 2 = 10 to the power of ?
a A LaTex expression showing ?=13
b A LaTex expression showing ?=6
c A LaTex expression showing ?=9
d A LaTex expression showing ?=15
e A LaTex expression showing ?=5
f A LaTex expression showing ?=8
2
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 3 = 10 to the power of ?
a A LaTex expression showing ?=12
b A LaTex expression showing ?=11
c A LaTex expression showing ?=1
d A LaTex expression showing ?=10
e A LaTex expression showing ?=2
f A LaTex expression showing ?=6
3
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 3 = 10 to the power of ?
a A LaTex expression showing ?=3
b A LaTex expression showing ?=18
c A LaTex expression showing ?=7
d A LaTex expression showing ?=9
e A LaTex expression showing ?=1
f A LaTex expression showing ?=6
4
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 4 ) to the power of 3 = 10 to the power of ?
a A LaTex expression showing ?=7
b A LaTex expression showing ?=19
c A LaTex expression showing ?=4
d A LaTex expression showing ?=12
e A LaTex expression showing ?=8
f A LaTex expression showing ?=13
5
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 2 = 10 to the power of ?
a A LaTex expression showing ?=2
b A LaTex expression showing ?=6
c A LaTex expression showing ?=1
d A LaTex expression showing ?=4
e A LaTex expression showing ?=8
f A LaTex expression showing ?=12
6
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 2 = 10 to the power of ?
a A LaTex expression showing ?=13
b A LaTex expression showing ?=11
c A LaTex expression showing ?=12
d A LaTex expression showing ?=2
e A LaTex expression showing ?=10
f A LaTex expression showing ?=6