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

This topic involves solving for missing exponents given equations where powers of numbers are equated to other expressions with exponents. The skills practiced include manipulating equations involving bases raised to variable and unknown powers, applying exponent rules, and simplifying expressions to find the value of unknown exponents. These problems are foundational in understanding the power laws of exponents, specifically handling composite bases with variable powers and translating them to exponent bases with unknown powers.

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

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Power Law - Composite Base with Variable Power to Exponent 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 (?) in reduced form

9n=(34)?9^{n} = (3^{4})^{?}

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

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Math worksheet on 'Exponents - Power Law - Composite Base with Variable Power to Exponent Base with Unknown 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 16 to the power of n = (2 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=2 over 2n
b A LaTex expression showing ?=6n
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=4 over 12n
e A LaTex expression showing ?=6n over 4
f A LaTex expression showing ?=4n over 12
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 27 to the power of n = (3 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=3n over 2
b A LaTex expression showing ?=9n over 2
c A LaTex expression showing ?=3n over 9
d A LaTex expression showing ?=6n over 3
e A LaTex expression showing ?=6n
f A LaTex expression showing ?=6 over 3n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 32 to the power of n = (2 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=2 over 2n
b A LaTex expression showing ?=5n over 10
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=4n over 5
e A LaTex expression showing ?=5n
f A LaTex expression showing ?=5n over 2
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 8 to the power of n = (2 to the power of 4 ) to the power of ?
a A LaTex expression showing ?=3n over 4
b A LaTex expression showing ?=5n
c A LaTex expression showing ?=3n over 6
d A LaTex expression showing ?=2 over 4n
e A LaTex expression showing ?=4n
f A LaTex expression showing ?=3n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 16 to the power of n = (4 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=3n
c A LaTex expression showing ?=2n over 3
d A LaTex expression showing ?=2 over 4n
e A LaTex expression showing ?=2n over 4
f A LaTex expression showing ?=6n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = (2 to the power of 5 ) to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=2 over 4n
c A LaTex expression showing ?=10n
d A LaTex expression showing ?=5n
e A LaTex expression showing ?=2n over 5
f A LaTex expression showing ?=2 over 5n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 81 to the power of n = (3 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=4n over 3
b A LaTex expression showing ?=6 over 4n
c A LaTex expression showing ?=6n
d A LaTex expression showing ?=7n
e A LaTex expression showing ?=3n over 3
f A LaTex expression showing ?=6n over 4