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

This math topic focuses on solving for unknown exponents within equations involving power laws and different bases, particularly powers of ten. These problems require understanding how exponents work when changing the base or manipulating powers of numbers like 10, 100, 1000, and 10000. Students practice converting expressions between these bases and solving for missing exponent values using the power rule, an essential part of exponents involving negative, fractional, and exponential laws.

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

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Power Law - Exponent 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 (?)

(103)8=10000?(10^{3})^{8} = 10000^{?}

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

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Math worksheet on 'Exponents - Power Law - Exponent 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 3 ) to the power of 8 = 10000 to the power of ?
a A LaTex expression showing ?=1
b A LaTex expression showing ?=10
c A LaTex expression showing ?=9
d A LaTex expression showing ?=6
e A LaTex expression showing ?=15
f A LaTex expression showing ?=3
2
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 12 = 10000 to the power of ?
a A LaTex expression showing ?=7
b A LaTex expression showing ?=17
c A LaTex expression showing ?=9
d A LaTex expression showing ?=4
e A LaTex expression showing ?=3
f A LaTex expression showing ?=10
3
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 ?=6
b A LaTex expression showing ?=5
c A LaTex expression showing ?=8
d A LaTex expression showing ?=10
e A LaTex expression showing ?=11
f A LaTex expression showing ?=4
4
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 ?=15
b A LaTex expression showing ?=6
c A LaTex expression showing ?=2
d A LaTex expression showing ?=12
e A LaTex expression showing ?=7
f A LaTex expression showing ?=5
5
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 12 = 10000 to the power of ?
a A LaTex expression showing ?=9
b A LaTex expression showing ?=3
c A LaTex expression showing ?=6
d A LaTex expression showing ?=2
e A LaTex expression showing ?=14
f A LaTex expression showing ?=11
6
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 ?=8
b A LaTex expression showing ?=3
c A LaTex expression showing ?=9
d A LaTex expression showing ?=12
e A LaTex expression showing ?=14
f A LaTex expression showing ?=13
7
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 6 = 100 to the power of ?
a A LaTex expression showing ?=3
b A LaTex expression showing ?=16
c A LaTex expression showing ?=9
d A LaTex expression showing ?=4
e A LaTex expression showing ?=8
f A LaTex expression showing ?=14