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

This math topic focuses on solving equations using the power law in exponents. Specifically, students practice finding an unknown exponent in expressions where both the exponent base and the powers are variable but partially known. Each problem presents an equation involving exponents, requiring the student to solve for the missing exponent in reduced form, applying their understanding of properties of exponents and algebraic manipulation skills.

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 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 (?) in reduced form

(3n)6=(3?)12(3^{n})^{6} = (3^{?})^{12}

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

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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 - Multiplication and Division - Advanced' Learn online: app.mobius.academy/math/units/exponents_multiplication_and_division_advanced/
1
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 6 = (3 to the power of ? ) to the power of 8
a A LaTex expression showing ?=4n
b A LaTex expression showing ?=7n
c A LaTex expression showing ?=4n over 8
d A LaTex expression showing ?=4 over 8n
e A LaTex expression showing ?=3n over 4
f A LaTex expression showing ?=3n over 3
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 10 = (2 to the power of ? ) to the power of 8
a A LaTex expression showing ?=6n
b A LaTex expression showing ?=4n over 8
c A LaTex expression showing ?=5n
d A LaTex expression showing ?=10 over 4n
e A LaTex expression showing ?=4 over 8n
f A LaTex expression showing ?=5n over 4
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 15 = (2 to the power of ? ) to the power of 12
a A LaTex expression showing ?=12n over 5
b A LaTex expression showing ?=4n
c A LaTex expression showing ?=5n over 4
d A LaTex expression showing ?=20n
e A LaTex expression showing ?=2n over 5
f A LaTex expression showing ?=15n over 4
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 15 = (2 to the power of ? ) to the power of 9
a A LaTex expression showing ?=2 over 5n
b A LaTex expression showing ?=9n over 5
c A LaTex expression showing ?=5n over 3
d A LaTex expression showing ?=5n
e A LaTex expression showing ?=15 over 3n
f A LaTex expression showing ?=3n over 9
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 8 = (3 to the power of ? ) to the power of 4
a A LaTex expression showing ?=5n
b A LaTex expression showing ?=4n
c A LaTex expression showing ?=3n over 4
d A LaTex expression showing ?=8n
e A LaTex expression showing ?=2n
f A LaTex expression showing ?=8 over 2n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 6 = (3 to the power of ? ) to the power of 9
a A LaTex expression showing ?=6 over 3n
b A LaTex expression showing ?=3n over 9
c A LaTex expression showing ?=6n
d A LaTex expression showing ?=2n over 3
e A LaTex expression showing ?=3n over 2
f A LaTex expression showing ?=8n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 6 = (3 to the power of ? ) to the power of 4
a A LaTex expression showing ?=3n over 2
b A LaTex expression showing ?=6n over 2
c A LaTex expression showing ?=3n
d A LaTex expression showing ?=2n over 4
e A LaTex expression showing ?=4n over 3
f A LaTex expression showing ?=3n over 3