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

This math topic focuses on the application of exponentiation and the power law which involves solving for missing exponents in equations that have bases of ten. Each question presents an equation where a power of ten is equated to a power of another power of ten, with the goal of determining the missing exponent. Simplification and understanding the relationship between the base and the exponent in expressions of powers of ten are central skills practiced here. This set of problems is a part of a broader unit on exponents which also includes negative and fractional exponents alongside power laws.

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 Unknown Exponent Base with Known Power

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Solve for the missing exponent (?)

10012=(10?)6100^{12} = (10^{?})^{6}

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

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