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

This math topic focuses on practicing the power law of exponents, specifically working with a base of ten. Students are tasked with solving for unknown exponents when bases are converted between forms, such as from 10 to 1000 or 100 to 10000. The problems require understanding how to equate different powers of ten and solve for the missing exponent that makes the equations true. This is part of a broader study on exponents that includes negative and fractional exponents, helping students develop a more comprehensive understanding of exponentiation rules and applications.

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 Power of 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 (?)

106=100?10^{6} = 100^{?}

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

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