Power Law - Which is Larger With Shared Factor in Exponent (Level 3)

This math topic focuses on applying the power law of exponents to determine which of two exponential expressions is larger when they share a common factor in their exponents. It involves problems that require comparing values of exponential functions with different bases and exponents. These problems enhance understanding of how exponential growth rates vary with changes in base and exponent, providing practice in evaluating and analyzing exponential expressions critically. This topic is part of a broader unit covering negative, fractional, and power law aspects of exponents.

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

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Exponents - Power Law - Which is Larger With Shared Factor in Exponent Worksheet

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Math worksheet on 'Exponents - Power Law - Which is Larger With Shared Factor in Exponent (Level 3)'. Part of a broader unit on 'Exponents - Negative, Fractional, and Power Law' Learn online: app.mobius.academy/math/units/exponents_negatives_fractions_and_power_law/
1
A LaTex expression showing 3 to the power of 231 \text{ or } 2 to the power of 385
Which is larger?
a A LaTex expression showing 3 to the power of 231
b A LaTex expression showing 2 to the power of 385
2
A LaTex expression showing 3 to the power of 198 \text{ or } 2 to the power of 330
Which is larger?
a A LaTex expression showing 2 to the power of 330
b A LaTex expression showing 3 to the power of 198
3
A LaTex expression showing 3 to the power of 99 \text{ or } 5 to the power of 66
Which is larger?
a A LaTex expression showing 3 to the power of 99
b A LaTex expression showing 5 to the power of 66
4
A LaTex expression showing 2 to the power of 231 \text{ or } 5 to the power of 99
Which is larger?
a A LaTex expression showing 2 to the power of 231
b A LaTex expression showing 5 to the power of 99
5
A LaTex expression showing 11 to the power of 88 \text{ or } 5 to the power of 132
Which is larger?
a A LaTex expression showing 5 to the power of 132
b A LaTex expression showing 11 to the power of 88
6
A LaTex expression showing 2 to the power of 330 \text{ or } 3 to the power of 198
Which is larger?
a A LaTex expression showing 2 to the power of 330
b A LaTex expression showing 3 to the power of 198
7
A LaTex expression showing 2 to the power of 165 \text{ or } 3 to the power of 110
Which is larger?
a A LaTex expression showing 3 to the power of 110
b A LaTex expression showing 2 to the power of 165