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Exponents - Power Law with Variable Base (Negatives, Exponent with Power to Fraction with Power) (Level 1)

This math topic focuses on mastering the exponent power laws, particularly with negative exponents and their application in simplifying expressions involving the multiplication of like bases presented in variable or negative exponential forms. The problems specifically emphasize on resolving expressions where variables are raised to negative powers and sometimes involve multiplying variables raised to fractional powers. The concepts are aimed at enhancing understanding of power rules and handling variables with negative and fractional exponents. Each problem requires identifying the correct simplified form from multiple choices provided.

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

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Power Law with Variable Base (Negatives, Exponent with Power to Fraction with Power)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Find the answer when these terms are multiplied

n−3⋅n−3⋅n−3⋅n−3n^{-3} \cdot n^{-3} \cdot n^{-3} \cdot n^{-3}

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

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Math worksheet on 'Exponents - Power Law with Variable Base (Negatives, Exponent with Power to Fraction with Power) (Level 1)'. Part of a broader unit on 'Exponents - Multiplication and Division - Advanced' Learn online: app.mobius.academy/math/units/exponents_multiplication_and_division_advanced/
1
Find the answer when these terms are multiplied
A LaTex expression showing r to the power of -1 times r to the power of -1 times r to the power of -1 times r to the power of -1
a A LaTex expression showing 1 over r to the power of 3
b A LaTex expression showing 1 over r to the power of 4
c A LaTex expression showing r to the power of 0
d A LaTex expression showing r to the power of 3
2
Find the answer when these terms are multiplied
A LaTex expression showing p to the power of -1 times p to the power of -1 times p to the power of -1 times p to the power of -1
a A LaTex expression showing p to the power of 3
b A LaTex expression showing 1 over p to the power of 3
c A LaTex expression showing 1 over p to the power of 4
d A LaTex expression showing p to the power of 0
3
Find the answer when these terms are multiplied
A LaTex expression showing y to the power of -3 times y to the power of -3 times y to the power of -3 times y to the power of -3
a A LaTex expression showing y
b A LaTex expression showing 1 over y to the power of 12
c A LaTex expression showing y to the power of 0
d A LaTex expression showing 1 over y
4
Find the answer when these terms are multiplied
A LaTex expression showing b to the power of -1 times b to the power of -1
a A LaTex expression showing 1 over b to the power of 200
b A LaTex expression showing 1 over b to the power of 2
c A LaTex expression showing 1 over b
d A LaTex expression showing 1
5
Find the answer when these terms are multiplied
A LaTex expression showing m to the power of -3 times m to the power of -3 times m to the power of -3
a A LaTex expression showing 1 over m to the power of 9
b A LaTex expression showing 1 over m to the power of 7
c A LaTex expression showing 1 over m to the power of 90
d A LaTex expression showing 1 over m to the power of 10
6
Find the answer when these terms are multiplied
A LaTex expression showing b to the power of -3 times b to the power of -3
a A LaTex expression showing 1 over b to the power of 6
b A LaTex expression showing b to the power of 0
c A LaTex expression showing 1 over b to the power of 5
d A LaTex expression showing 1 over b to the power of 600
e A LaTex expression showing 1 over b to the power of 60
7
Find the answer when these terms are multiplied
A LaTex expression showing n to the power of -2 times n to the power of -2 times n to the power of -2
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 5
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 6