Power Law - Algebra (Base of X is Power) (Level 1)

This math topic covers the application of the power law in algebra involving exponents, where the bases can be variables or fractions raised to an exponent. The students are asked to solve equations where they determine the value of unknown exponents by equating and simplifying expressions with like bases. It is aimed at deepening understanding of how to manipulate and solve equations dealing with powers and roots, an essential skill set in the broader unit concerning exponents, including negative and fractional exponent rules.

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

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Exponents - Power Law - Algebra (Base of X is Power) Worksheet

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Math worksheet on 'Exponents - Power Law - Algebra (Base of X is Power) (Level 1)'. Part of a broader unit on 'Exponents - Negative, Fractional, and Power Law' Learn online: app.mobius.academy/math/units/exponents_negatives_fractions_and_power_law/
1
Solve for x
A LaTex expression showing 121 to the power of x = 11 to the power of 2
a A LaTex expression showing x=8
b A LaTex expression showing x=2
c A LaTex expression showing x=3
d A LaTex expression showing x=9
e A LaTex expression showing x=1
f A LaTex expression showing x=10
2
Solve for x
A LaTex expression showing 4 to the power of x = 2 to the power of 16
a A LaTex expression showing x=17
b A LaTex expression showing x=6
c A LaTex expression showing x=8
d A LaTex expression showing x=3
e A LaTex expression showing x=2
f A LaTex expression showing x=11
3
Solve for x
A LaTex expression showing 121 to the power of x = 11 to the power of 6
a A LaTex expression showing x=12
b A LaTex expression showing x=7
c A LaTex expression showing x=9
d A LaTex expression showing x=6
e A LaTex expression showing x=3
f A LaTex expression showing x=5
4
Solve for x
A LaTex expression showing 9 to the power of x = 3 to the power of 10
a A LaTex expression showing x=14
b A LaTex expression showing x=6
c A LaTex expression showing x=4
d A LaTex expression showing x=5
e A LaTex expression showing x=7
f A LaTex expression showing x=9
5
Solve for x
A LaTex expression showing 49 to the power of x = 7 to the power of 2
a A LaTex expression showing x=1
b A LaTex expression showing x=10
c A LaTex expression showing x=4
d A LaTex expression showing x=7
e A LaTex expression showing x=9
f A LaTex expression showing x=8
6
Solve for x
A LaTex expression showing 9 to the power of x = 3 to the power of 16
a A LaTex expression showing x=8
b A LaTex expression showing x=3
c A LaTex expression showing x=2
d A LaTex expression showing x=11
e A LaTex expression showing x=5
f A LaTex expression showing x=16
7
Solve for x
A LaTex expression showing 121 to the power of x = 11 to the power of 20
a A LaTex expression showing x=10
b A LaTex expression showing x=6
c A LaTex expression showing x=18
d A LaTex expression showing x=13
e A LaTex expression showing x=17
f A LaTex expression showing x=11