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Exponents

Power Law - Which is Larger With Shared Factor in Exponent (Level 1)

This math topic focuses on comparing the magnitudes of numbers expressed with large exponents. It involves evaluating which of two given exponential expressions is larger, where base numbers and their exponents differ. Specific scenarios include comparing numbers such as \(11^{200}\) versus \(5^{300}\), or \(2^{5000}\) versus \(3^{3000}\). This topic is a part of a broader unit on negative, fractional, and power laws of exponents, helping students develop their skills in understanding and manipulating exponential expressions in various contexts.

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 1)'. 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 11 to the power of 200 \text{ or } 5 to the power of 300
Which is larger?
a A LaTex expression showing 5 to the power of 300
b A LaTex expression showing 11 to the power of 200
2
A LaTex expression showing 5 to the power of 30 \text{ or } 11 to the power of 20
Which is larger?
a A LaTex expression showing 5 to the power of 30
b A LaTex expression showing 11 to the power of 20
3
A LaTex expression showing 2 to the power of 5000 \text{ or } 3 to the power of 3000
Which is larger?
a A LaTex expression showing 2 to the power of 5000
b A LaTex expression showing 3 to the power of 3000
4
A LaTex expression showing 11 to the power of 20 \text{ or } 5 to the power of 30
Which is larger?
a A LaTex expression showing 11 to the power of 20
b A LaTex expression showing 5 to the power of 30
5
A LaTex expression showing 2 to the power of 7000 \text{ or } 11 to the power of 2000
Which is larger?
a A LaTex expression showing 2 to the power of 7000
b A LaTex expression showing 11 to the power of 2000
6
A LaTex expression showing 2 to the power of 140 \text{ or } 5 to the power of 60
Which is larger?
a A LaTex expression showing 2 to the power of 140
b A LaTex expression showing 5 to the power of 60
7
A LaTex expression showing 2 to the power of 30 \text{ or } 3 to the power of 20
Which is larger?
a A LaTex expression showing 2 to the power of 30
b A LaTex expression showing 3 to the power of 20