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

This math topic focuses on applying the power law of exponents, specifically involving a power of ten base with a variable exponent. It includes exercises where learners solve for unknown exponents by equating powers of 10 represented in two different forms. This is a particular part of a broader topic on negative, fractional, and power laws of exponents. The problems require learners to rearrange and solve exponential equations, which enhances their skills in working with powers and algebraic manipulation.

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

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Power Law - Power of 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 (?)

100009=(103)?10000^{9} = (10^{3})^{?}

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

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Math worksheet on 'Exponents - Power Law - Power of 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 10000 to the power of 9 = (10 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=5
b A LaTex expression showing ?=12
c A LaTex expression showing ?=21
d A LaTex expression showing ?=9
e A LaTex expression showing ?=19
f A LaTex expression showing ?=14
2
Solve for the missing exponent (?)
A LaTex expression showing 100 to the power of 9 = (10 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=2
b A LaTex expression showing ?=12
c A LaTex expression showing ?=3
d A LaTex expression showing ?=4
e A LaTex expression showing ?=6
f A LaTex expression showing ?=15
3
Solve for the missing exponent (?)
A LaTex expression showing 1000 to the power of 6 = (10 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=4
b A LaTex expression showing ?=1
c A LaTex expression showing ?=9
d A LaTex expression showing ?=16
e A LaTex expression showing ?=13
f A LaTex expression showing ?=14
4
Solve for the missing exponent (?)
A LaTex expression showing 1000 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 ?=15
c A LaTex expression showing ?=7
d A LaTex expression showing ?=3
e A LaTex expression showing ?=9
f A LaTex expression showing ?=13
5
Solve for the missing exponent (?)
A LaTex expression showing 100 to the power of 6 = (10 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=7
b A LaTex expression showing ?=5
c A LaTex expression showing ?=4
d A LaTex expression showing ?=12
e A LaTex expression showing ?=8
f A LaTex expression showing ?=6
6
Solve for the missing exponent (?)
A LaTex expression showing 1000 to the power of 4 = (10 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=4
b A LaTex expression showing ?=11
c A LaTex expression showing ?=2
d A LaTex expression showing ?=12
e A LaTex expression showing ?=1
f A LaTex expression showing ?=6
7
Solve for the missing exponent (?)
A LaTex expression showing 100 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 ?=8
c A LaTex expression showing ?=6
d A LaTex expression showing ?=13
e A LaTex expression showing ?=10
f A LaTex expression showing ?=14