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

This math topic focuses on practicing the Power Law of exponents involving calculations with variable bases raised to given powers equated to the same bases raised to unknown powers. The problems require solving for missing exponents represented by a '?'. Each problem is structured with multiple choice answers, varying expressions for the potential value of the questioned exponent, challenging the student to apply exponent rules properly to find the correct simplified expression. This is part of a broader introduction to exponentiation rules, targeting fundamental algebraic skills in handling powers and exponents.

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 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

(2n)9=(23)?(2^{n})^{9} = (2^{3})^{?}

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

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Math worksheet on 'Exponents - Power Law - Variable Exponent Base with Known 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 (2 to the power of n ) to the power of 15 = (2 to the power of 5 ) to the power of ?
a A LaTex expression showing ?=20n
b A LaTex expression showing ?=2 over 5n
c A LaTex expression showing ?=2n over 5
d A LaTex expression showing ?=5n
e A LaTex expression showing ?=15n over 4
f A LaTex expression showing ?=3n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 12 = (3 to the power of 4 ) to the power of ?
a A LaTex expression showing ?=3 over 9n
b A LaTex expression showing ?=12n
c A LaTex expression showing ?=6n
d A LaTex expression showing ?=3n over 4
e A LaTex expression showing ?=12n over 3
f A LaTex expression showing ?=3n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 12 = (2 to the power of 4 ) to the power of ?
a A LaTex expression showing ?=12n over 5
b A LaTex expression showing ?=5 over 15n
c A LaTex expression showing ?=15n over 4
d A LaTex expression showing ?=5n
e A LaTex expression showing ?=3n
f A LaTex expression showing ?=4n
4
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 4 ) to the power of ?
a A LaTex expression showing ?=4n
b A LaTex expression showing ?=8n over 2
c A LaTex expression showing ?=8n
d A LaTex expression showing ?=2n
e A LaTex expression showing ?=4n over 4
f A LaTex expression showing ?=3n over 4
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 6 = (2 to the power of 3 ) to the power of ?
a A LaTex expression showing ?=9n
b A LaTex expression showing ?=2 over 3n
c A LaTex expression showing ?=6n over 2
d A LaTex expression showing ?=2n
e A LaTex expression showing ?=6n
f A LaTex expression showing ?=2 over 4n
6
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 5 ) to the power of ?
a A LaTex expression showing ?=10n over 2
b A LaTex expression showing ?=2n
c A LaTex expression showing ?=4n over 5
d A LaTex expression showing ?=2 over 5n
e A LaTex expression showing ?=2 over 4n
f A LaTex expression showing ?=15n
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 4 = (2 to the power of 2 ) to the power of ?
a A LaTex expression showing ?=2n
b A LaTex expression showing ?=4 over 8n
c A LaTex expression showing ?=6n
d A LaTex expression showing ?=2n over 2
e A LaTex expression showing ?=2 over 2n
f A LaTex expression showing ?=8n over 2