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

This topic focuses on practicing the application of the Power Law of Exponents with variables. The exercises involve multiplying expressions with negative and fraction exponents, calculating the resulting exponents, and selecting the correct result from multiple choices. The main skills sharpened here include managing powers of negative and fractional exponents, particularly in a variable base setting. Each question provides a different expression, containing varying complexities of base and exponent manipulation, allowing for a comprehensive understanding and handling of exponent rules.

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, Fraction with Power to Exponent)

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

Find the answer when these terms are multiplied

1b4â‹…1b4\frac{1}{b^{4}} \cdot \frac{1}{b^{4}}

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

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Math worksheet on 'Exponents - Power Law with Variable Base (Negatives, Fraction with Power to Exponent) (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 1 over r to the power of 5 times 1 over r to the power of 5 times 1 over r to the power of 5 times 1 over r to the power of 5 times 1 over r to the power of 5 times 1 over r to the power of 5
a A LaTex expression showing r
b A LaTex expression showing r to the power of -300
c A LaTex expression showing r to the power of -30
d A LaTex expression showing r to the power of -28
2
Find the answer when these terms are multiplied
A LaTex expression showing 1 over b to the power of 3 times 1 over b to the power of 3 times 1 over b to the power of 3 times 1 over b to the power of 3 times 1 over b to the power of 3 times 1 over b to the power of 3
a A LaTex expression showing b to the power of 3
b A LaTex expression showing b to the power of -18
c A LaTex expression showing b to the power of -15
3
Find the answer when these terms are multiplied
A LaTex expression showing 1 over p to the power of 5 times 1 over p to the power of 5 times 1 over p to the power of 5 times 1 over p to the power of 5 times 1 over p to the power of 5
a A LaTex expression showing p to the power of -29
b A LaTex expression showing p to the power of -21
c A LaTex expression showing p to the power of -28
d A LaTex expression showing p to the power of -25
e A LaTex expression showing p to the power of 0
4
Find the answer when these terms are multiplied
A LaTex expression showing 1 over x to the power of 3 times 1 over x to the power of 3
a A LaTex expression showing x to the power of -6
b A LaTex expression showing x to the power of -7
c A LaTex expression showing x to the power of -1
d A LaTex expression showing x to the power of -60
5
Find the answer when these terms are multiplied
A LaTex expression showing 1 over x to the power of 4 times 1 over x to the power of 4 times 1 over x to the power of 4 times 1 over x to the power of 4
a A LaTex expression showing x to the power of 0
b A LaTex expression showing x to the power of -1
c A LaTex expression showing x to the power of -15
d A LaTex expression showing x to the power of -14
e A LaTex expression showing x to the power of -16
6
Find the answer when these terms are multiplied
A LaTex expression showing 1 over d to the power of 2 times 1 over d to the power of 2 times 1 over d to the power of 2 times 1 over d to the power of 2 times 1 over d to the power of 2 times 1 over d to the power of 2
a A LaTex expression showing d to the power of -10
b A LaTex expression showing d to the power of -1
c A LaTex expression showing d to the power of -12
d A LaTex expression showing d to the power of 4
7
Find the answer when these terms are multiplied
A LaTex expression showing 1 over b to the power of 4 times 1 over b to the power of 4
a A LaTex expression showing b to the power of 0
b A LaTex expression showing b to the power of -8
c A LaTex expression showing b to the power of -2
d A LaTex expression showing b to the power of -80