Power Law with Variable Base (Negatives, Expanded Fraction to Fraction with Power) (Level 1)

This math topic focuses on practicing the power law of exponents with variable bases, particularly involving negative exponents and the conversion of expanded fractions to powers of fractions. The detailed problems are centered on multiplying terms that include fractional bases raised to various powers, requiring skills in manipulating exponents to simplify expressions. These questions are suited for students starting to learn about the power properties of exponents in an introductory unit on the topic. Multiple-choice answers are provided to verify comprehension and correctness of exponential manipulations.

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

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Exponents - Power Law with Variable Base (Negatives, Expanded Fraction to Fraction with Power) Worksheet

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Exponents - Power Law with Variable Base (Negatives, Expanded Fraction to Fraction with Power)
1
Find the answer when these terms are multiplied
A LaTex expression showing 1 over m to the power of 2 times 1 over m to the power of 2 times 1 over m to the power of 2 times 1 over m to the power of 2
a A LaTex expression showing 1 over m to the power of 800
b A LaTex expression showing 1 over m to the power of 8
c A LaTex expression showing 1 over m to the power of 6
2
Find the answer when these terms are multiplied
A LaTex expression showing 1 over n times 1 over n times 1 over n times 1 over n
a A LaTex expression showing 1 over n to the power of 4
b A LaTex expression showing 1 over n to the power of 3
c A LaTex expression showing 1 over n to the power of 400
d A LaTex expression showing n to the power of 3
3
Find the answer when these terms are multiplied
A LaTex expression showing 1 over n to the power of 2 times 1 over n to the power of 2 times 1 over n to the power of 2
a A LaTex expression showing n
b A LaTex expression showing 1 over n to the power of 6
c A LaTex expression showing 1 over n to the power of 600
d A LaTex expression showing n to the power of 0
e A LaTex expression showing 1 over n to the power of 60
4
Find the answer when these terms are multiplied
A LaTex expression showing 1 over b times 1 over b times 1 over b times 1 over b
a A LaTex expression showing b to the power of 3
b A LaTex expression showing 1 over b to the power of 4
c A LaTex expression showing 1
d A LaTex expression showing b to the power of 0
e A LaTex expression showing 1 over b to the power of 400
5
Find the answer when these terms are multiplied
A LaTex expression showing 1 over d to the power of 3 times 1 over d to the power of 3 times 1 over d to the power of 3
a A LaTex expression showing d to the power of 0
b A LaTex expression showing 1 over d to the power of 900
c A LaTex expression showing 1 over d to the power of 9
d A LaTex expression showing 1 over d to the power of 10
e A LaTex expression showing 1 over d to the power of 7
6
Find the answer when these terms are multiplied
A LaTex expression showing 1 over z to the power of 2 times 1 over z to the power of 2
a A LaTex expression showing 1 over z to the power of 3
b A LaTex expression showing z to the power of 0
c A LaTex expression showing 1 over z to the power of 4
d A LaTex expression showing 1
7
Find the answer when these terms are multiplied
A LaTex expression showing 1 over n times 1 over n times 1 over n
a A LaTex expression showing n to the power of 0
b A LaTex expression showing 1 over n to the power of 3
c A LaTex expression showing n to the power of 2
d A LaTex expression showing 1 over n to the power of 2
e A LaTex expression showing 1 over n to the power of 300
8
Find the answer when these terms are multiplied
A LaTex expression showing 1 over r to the power of 3 times 1 over r to the power of 3 times 1 over r to the power of 3 times 1 over r to the power of 3
a A LaTex expression showing 1 over r to the power of 120
b A LaTex expression showing 1 over r to the power of 12
c A LaTex expression showing 1 over r to the power of 1,200
d A LaTex expression showing r
e A LaTex expression showing 1