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

This math topic focuses on applying the power law of exponents to solve for unknown powers. Students utilize algebraic methods to determine the exponent in equations where bases with variable and unknown powers are equated. Problems include converting expressions with multiple levels of exponentiation into their simplest forms and solving for the missing exponent values. The exercises involve recognizing and manipulating bases and their powers to establish equivalence between the two sides of an equation, enhancing students' algebraic proficiency and understanding of exponent rules.

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 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

(24)n=(25)?(2^{4})^{n} = (2^{5})^{?}

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

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Math worksheet on 'Exponents - Power Law - Exponent 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 (3 to the power of 3 ) to the power of n = (3 to the power of 4 ) to the power of ?
a A LaTex expression showing ?=3n over 4
b A LaTex expression showing ?=16n
c A LaTex expression showing ?=3 over 4n
d A LaTex expression showing ?=12n over 3
e A LaTex expression showing ?=3n over 9
f A LaTex expression showing ?=12n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (4 to the power of 2 ) to the power of n = (4 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=3n
b A LaTex expression showing ?=2n over 3
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=4n over 3
e A LaTex expression showing ?=6n
f A LaTex expression showing ?=9n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (4 to the power of 3 ) to the power of n = (4 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=6n
b A LaTex expression showing ?=2n
c A LaTex expression showing ?=3 over 9n
d A LaTex expression showing ?=3n
e A LaTex expression showing ?=6 over 3n
f A LaTex expression showing ?=3n over 2
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 4 ) to the power of n = (2 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=2n over 2
c A LaTex expression showing ?=8n over 2
d A LaTex expression showing ?=6n
e A LaTex expression showing ?=4 over 8n
f A LaTex expression showing ?=4 over 4n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of 4 ) to the power of n = (3 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=4n over 12
c A LaTex expression showing ?=4n
d A LaTex expression showing ?=6n
e A LaTex expression showing ?=3n over 2
f A LaTex expression showing ?=6n over 4
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 4 ) to the power of n = (2 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=3n
b A LaTex expression showing ?=4n over 3
c A LaTex expression showing ?=4n
d A LaTex expression showing ?=2 over 3n
e A LaTex expression showing ?=9n over 4
f A LaTex expression showing ?=12n over 3
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of 3 ) to the power of n = (2 to the power of 5 ) to the power of ?
a A LaTex expression showing ?=15n
b A LaTex expression showing ?=5n
c A LaTex expression showing ?=20n
d A LaTex expression showing ?=3 over 9n
e A LaTex expression showing ?=3n over 5
f A LaTex expression showing ?=2 over 5n