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

This math topic focuses on practicing how to solve for missing exponents using the Power Law of exponents, specifically with a base of ten. The problems involve determining what the exponent should be when a base-ten number raised to a certain power equals another base-ten number raised to another power, which is then raised to a missing exponent. This topic is a part of a broader unit on negative, fractional, and power laws of exponents. Each question provides multiple choice answers, allowing students to select the correct missing exponent.

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

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Power Law - Ten 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 (?)

106=(102)?10^{6} = (10^{2})^{?}

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

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