HomePricing
Sign InJoin

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

This math topic focuses on applying the power law of exponents to find missing exponents. Specifically, the problems present scenarios where the variable exponent base is known, and learners must determine the unknown exponent base that equates to a given power. The problems use numerical base 10 raised to a power, which is then further raised to an exponent, and set equal to the base 10 raised to an unknown exponent and then raised to another given exponent. The goal is to solve for the unknown exponent by manipulating the properties of exponents in expressions of base 10.

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

View Unit

Power Law - Variable Exponent Base with Known 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 (?)

(102)8=(10?)4(10^{2})^{8} = (10^{?})^{4}

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

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