Power of Percentage

Algebra Level 3

Which of the following numbers is the largest?

( 20 % ) 3 ( 30 % ) 4 ( 40 % ) 5 ( 50 % ) 6 (20\%)^3 \qquad (30\%)^4 \qquad (40\%)^5 \qquad (50\%)^6

( 20 % ) 3 (20\%)^3 ( 30 % ) 4 (30\%)^4 ( 40 % ) 5 (40\%)^5 ( 50 % ) 6 (50\%)^6

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1 solution

Emily Namm
Jul 2, 2016

To convert percents into decimals, divide them by 100.

20% = 0.2

30% = 0.3

40% = 0.4

50% = 0.5

Next, evaluate.

0.2 cubed = 0.2 x 0.2 x 0.2 = 0.008

0.3^4 = 0.3 x 0.3 x 0.3 x 0.3 = 0.0081

0.4^5 = 0.4 x 0.4 x 0.4 x 0.4 x 0.4 = 0.01024

0.5^6 = 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.015625

0.015625 > 0.01024 > 0.0081 > 0.008.

0.015625, or 50%^6, is the greatest.

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