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

This topic focuses on solving for the variable \( x \) in equations involving exponents, specifically using the power law. Each problem is structured around equating a base raised to the power of the square root of \( x \) to another exponential expression with a different base and exponent. The problems require utilizing properties of exponents and roots to isolate and solve for \( x \). Students are provided with multiple-choice answers, testing their ability to apply algebraic rules to manipulate and solve exponent equations effectively.

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 Constant is Power, Solve Root X) Worksheet

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Exponents - Power Law - Algebra (Base of Constant is Power, Solve Root X)
1
Solve for x
A LaTex expression showing 11 to the power of {square root of x } = 121 to the power of 6
a A LaTex expression showing x=158
b A LaTex expression showing x=81
c A LaTex expression showing x=4
d A LaTex expression showing x=49
e A LaTex expression showing x=200
f A LaTex expression showing x=144
2
Solve for x
A LaTex expression showing 3 to the power of {square root of x } = 9 to the power of 7
a A LaTex expression showing x=144
b A LaTex expression showing x=169
c A LaTex expression showing x=196
d A LaTex expression showing x=9
e A LaTex expression showing x=121
f A LaTex expression showing x=4
3
Solve for x
A LaTex expression showing 3 to the power of {square root of x } = 9 to the power of 5
a A LaTex expression showing x=4
b A LaTex expression showing x=100
c A LaTex expression showing x=64
d A LaTex expression showing x=130
e A LaTex expression showing x=25
f A LaTex expression showing x=196
4
Solve for x
A LaTex expression showing 5 to the power of {square root of x } = 25 to the power of 5
a A LaTex expression showing x=100
b A LaTex expression showing x=36
c A LaTex expression showing x=49
d A LaTex expression showing x=169
e A LaTex expression showing x=64
f A LaTex expression showing x=16
5
Solve for x
A LaTex expression showing 7 to the power of {square root of x } = 49 to the power of 2
a A LaTex expression showing x=15
b A LaTex expression showing x=16
c A LaTex expression showing x=121
d A LaTex expression showing x=4
e A LaTex expression showing x=7
f A LaTex expression showing x=9
6
Solve for x
A LaTex expression showing 5 to the power of {square root of x } = 25 to the power of 7
a A LaTex expression showing x=367
b A LaTex expression showing x=234
c A LaTex expression showing x=121
d A LaTex expression showing x=36
e A LaTex expression showing x=100
f A LaTex expression showing x=196
7
Solve for x
A LaTex expression showing 2 to the power of {square root of x } = 8 to the power of 2
a A LaTex expression showing x=36
b A LaTex expression showing x=100
c A LaTex expression showing x=9
d A LaTex expression showing x=25
e A LaTex expression showing x=81
f A LaTex expression showing x=42
8
Solve for x
A LaTex expression showing 11 to the power of {square root of x } = 121 to the power of 4
a A LaTex expression showing x=40
b A LaTex expression showing x=64
c A LaTex expression showing x=169
d A LaTex expression showing x=49
e A LaTex expression showing x=100
f A LaTex expression showing x=88