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

This topic focuses on applying the power law in exponents within an algebraic context, specifically when the base is a variable raised to a power, such as \(x^2\). It includes solving equations where variable bases with squared exponents are equated to constant expressions, requiring students to manipulate and simplify exponent expressions to find the values of \(x\). The worksheet exercises enhance students' ability to handle complex exponent rules and direct their algebraic acuity toward solving for variables in exponential equations, thereby integrating skills from both algebra and exponents areas.

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

more
View

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

Mobius Math Academy logo
Exponents - Power Law - Algebra (Base of X Squared is Power)
1
Solve for x
A LaTex expression showing 4 to the power of {(x^2) } = 2 to the power of 32
a A LaTex expression showing x=11
b A LaTex expression showing x=10
c A LaTex expression showing x=4
d A LaTex expression showing x=2
e A LaTex expression showing x=12
f A LaTex expression showing x=3
2
Solve for x
A LaTex expression showing 25 to the power of {(x^2) } = 5 to the power of 162
a A LaTex expression showing x=15
b A LaTex expression showing x=9
c A LaTex expression showing x=8
d A LaTex expression showing x=7
e A LaTex expression showing x=18
f A LaTex expression showing x=10
3
Solve for x
A LaTex expression showing 25 to the power of {(x^2) } = 5 to the power of 18
a A LaTex expression showing x=2
b A LaTex expression showing x=8
c A LaTex expression showing x=7
d A LaTex expression showing x=6
e A LaTex expression showing x=3
f A LaTex expression showing x=12
4
Solve for x
A LaTex expression showing 121 to the power of {(x^2) } = 11 to the power of 128
a A LaTex expression showing x=11
b A LaTex expression showing x=3
c A LaTex expression showing x=9
d A LaTex expression showing x=14
e A LaTex expression showing x=2
f A LaTex expression showing x=8
5
Solve for x
A LaTex expression showing 49 to the power of {(x^2) } = 7 to the power of 50
a A LaTex expression showing x=1
b A LaTex expression showing x=7
c A LaTex expression showing x=2
d A LaTex expression showing x=3
e A LaTex expression showing x=6
f A LaTex expression showing x=5
6
Solve for x
A LaTex expression showing 49 to the power of {(x^2) } = 7 to the power of 162
a A LaTex expression showing x=3
b A LaTex expression showing x=1
c A LaTex expression showing x=13
d A LaTex expression showing x=15
e A LaTex expression showing x=4
f A LaTex expression showing x=9
7
Solve for x
A LaTex expression showing 9 to the power of {(x^2) } = 3 to the power of 162
a A LaTex expression showing x=17
b A LaTex expression showing x=16
c A LaTex expression showing x=13
d A LaTex expression showing x=9
e A LaTex expression showing x=1
f A LaTex expression showing x=6
8
Solve for x
A LaTex expression showing 16 to the power of {(x^2) } = 2 to the power of 36
a A LaTex expression showing x=5
b A LaTex expression showing x=3
c A LaTex expression showing x=2
d A LaTex expression showing x=12
e A LaTex expression showing x=6
f A LaTex expression showing x=4