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

This math topic focuses on solving problems involving the power law of exponents. Specifically, students practice converting expressions with variable exponent bases and known powers to expressions with a base of ten and unknown powers. The problems typically involve finding the missing exponent in equalities where both sides have exponential forms but different bases, such as transforming expressions with base 10 raised to some power, to equivalent expressions with larger exponential bases like 100, 1000, or 10000. It is part of a broader unit covering negative, fractional, and power laws of exponents.

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

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Power Law - Variable Exponent Base with Known 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 (?)

(102)6=1000?(10^{2})^{6} = 1000^{?}

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

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Math worksheet on 'Exponents - Power Law - Variable Exponent Base with Known 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 4 ) to the power of 4 = 100 to the power of ?
a A LaTex expression showing ?=15
b A LaTex expression showing ?=8
c A LaTex expression showing ?=16
d A LaTex expression showing ?=13
e A LaTex expression showing ?=17
f A LaTex expression showing ?=11
2
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 6 = 1000 to the power of ?
a A LaTex expression showing ?=13
b A LaTex expression showing ?=12
c A LaTex expression showing ?=9
d A LaTex expression showing ?=3
e A LaTex expression showing ?=2
f A LaTex expression showing ?=4
3
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 4 ) to the power of 6 = 100 to the power of ?
a A LaTex expression showing ?=21
b A LaTex expression showing ?=12
c A LaTex expression showing ?=20
d A LaTex expression showing ?=6
e A LaTex expression showing ?=10
f A LaTex expression showing ?=11
4
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 8 = 10000 to the power of ?
a A LaTex expression showing ?=8
b A LaTex expression showing ?=11
c A LaTex expression showing ?=1
d A LaTex expression showing ?=5
e A LaTex expression showing ?=4
f A LaTex expression showing ?=2
5
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 4 = 100 to the power of ?
a A LaTex expression showing ?=5
b A LaTex expression showing ?=9
c A LaTex expression showing ?=6
d A LaTex expression showing ?=11
e A LaTex expression showing ?=1
f A LaTex expression showing ?=13
6
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 8 = 10000 to the power of ?
a A LaTex expression showing ?=11
b A LaTex expression showing ?=10
c A LaTex expression showing ?=2
d A LaTex expression showing ?=6
e A LaTex expression showing ?=12
f A LaTex expression showing ?=7
7
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 9 = 1000 to the power of ?
a A LaTex expression showing ?=7
b A LaTex expression showing ?=3
c A LaTex expression showing ?=15
d A LaTex expression showing ?=8
e A LaTex expression showing ?=6
f A LaTex expression showing ?=1