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

This math topic provides exercises on understanding and applying the power law of exponents, specifically focusing on equations where a power of 10 is raised to another power. Each problem presents an equation with a base of 10 raised to a variable exponent, which is then itself raised to another known exponent, and students are required to determine the missing exponent in the resultant expression. The practice helps reinforce concepts related to exponents, including how to handle variable exponents and basic exponentiation rules.

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 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)2=10?(10^{2})^{2} = 10^{?}

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

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Math worksheet on 'Exponents - Power Law - Variable Exponent Base with Known Power to 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 3 = 10 to the power of ?
a A LaTex expression showing ?=2
b A LaTex expression showing ?=6
c A LaTex expression showing ?=13
d A LaTex expression showing ?=17
e A LaTex expression showing ?=9
f A LaTex expression showing ?=11
2
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 4 ) to the power of 2 = 10 to the power of ?
a A LaTex expression showing ?=3
b A LaTex expression showing ?=9
c A LaTex expression showing ?=2
d A LaTex expression showing ?=15
e A LaTex expression showing ?=5
f A LaTex expression showing ?=8
3
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 2 = 10 to the power of ?
a A LaTex expression showing ?=2
b A LaTex expression showing ?=8
c A LaTex expression showing ?=4
d A LaTex expression showing ?=3
e A LaTex expression showing ?=5
f A LaTex expression showing ?=6
4
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 3 ) to the power of 2 = 10 to the power of ?
a A LaTex expression showing ?=4
b A LaTex expression showing ?=1
c A LaTex expression showing ?=11
d A LaTex expression showing ?=6
e A LaTex expression showing ?=3
f A LaTex expression showing ?=10
5
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 2 ) to the power of 3 = 10 to the power of ?
a A LaTex expression showing ?=2
b A LaTex expression showing ?=6
c A LaTex expression showing ?=10
d A LaTex expression showing ?=8
e A LaTex expression showing ?=11
f A LaTex expression showing ?=9
6
Solve for the missing exponent (?)
A LaTex expression showing (10 to the power of 4 ) to the power of 3 = 10 to the power of ?
a A LaTex expression showing ?=3
b A LaTex expression showing ?=12
c A LaTex expression showing ?=10
d A LaTex expression showing ?=7
e A LaTex expression showing ?=19
f A LaTex expression showing ?=17