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

This math topic focuses on applying the power law of exponents, particularly in cases where the base involves roots and algebraic manipulation. It is designed for those learning about negative, fractional, and power laws of exponents. The problems involve equations where learners must solve for the variable \( x \) by equating expressions with exponential and root functions, leveraging their understanding of how to manipulate exponents algebraically to isolate and determine \( x \). This is aimed at enhancing algebraic skills in handling powers and roots systematically.

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 Root X is Power) Worksheet

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Exponents - Power Law - Algebra (Base of Root X is Power)
1
Solve for x
A LaTex expression showing 121 to the power of {square root of x } = 11 to the power of 12
a A LaTex expression showing x=196
b A LaTex expression showing x=64
c A LaTex expression showing x=169
d A LaTex expression showing x=144
e A LaTex expression showing x=21
f A LaTex expression showing x=36
2
Solve for x
A LaTex expression showing 121 to the power of {square root of x } = 11 to the power of 20
a A LaTex expression showing x=144
b A LaTex expression showing x=100
c A LaTex expression showing x=121
d A LaTex expression showing x=16
e A LaTex expression showing x=49
f A LaTex expression showing x=81
3
Solve for x
A LaTex expression showing 121 to the power of {square root of x } = 11 to the power of 4
a A LaTex expression showing x=144
b A LaTex expression showing x=16
c A LaTex expression showing x=12
d A LaTex expression showing x=4
e A LaTex expression showing x=49
f A LaTex expression showing x=100
4
Solve for x
A LaTex expression showing 121 to the power of {square root of x } = 11 to the power of 22
a A LaTex expression showing x=49
b A LaTex expression showing x=25
c A LaTex expression showing x=121
d A LaTex expression showing x=100
e A LaTex expression showing x=217
f A LaTex expression showing x=196
5
Solve for x
A LaTex expression showing 49 to the power of {square root of x } = 7 to the power of 18
a A LaTex expression showing x=25
b A LaTex expression showing x=129
c A LaTex expression showing x=64
d A LaTex expression showing x=81
e A LaTex expression showing x=4
f A LaTex expression showing x=113
6
Solve for x
A LaTex expression showing 8 to the power of {square root of x } = 2 to the power of 3
a A LaTex expression showing x=196
b A LaTex expression showing x=121
c A LaTex expression showing x=25
d A LaTex expression showing x=144
e A LaTex expression showing x=1
f A LaTex expression showing x=2
7
Solve for x
A LaTex expression showing 4 to the power of {square root of x } = 2 to the power of 2
a A LaTex expression showing x=25
b A LaTex expression showing x=2
c A LaTex expression showing x=1
d A LaTex expression showing x=81
e A LaTex expression showing x=36
f A LaTex expression showing x=9
8
Solve for x
A LaTex expression showing 49 to the power of {square root of x } = 7 to the power of 20
a A LaTex expression showing x=144
b A LaTex expression showing x=121
c A LaTex expression showing x=100
d A LaTex expression showing x=49
e A LaTex expression showing x=10
f A LaTex expression showing x=36