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# how to write 4 x 16^2 as a single power of 2?

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- JimLv 78 months ago
4 × 16^2 = 1024 = 2^10

from 2^2 x (2^4)^2

= 2^2 x 2^8

= 2^(2+8)

= 2^10

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- PuzzlingLv 78 months ago
Write each base as a power of 2 first --> 4 = 2^2 and 16 = 2^4:

2^2 * (2^4)^2

Next use this rule of exponents --> (a^b)^c = a^(bc)

= 2^2 * 2^(4*2)

= 2^2 * 2^8

Then use this rule of exponents --> a^b * a^c = a^(b+c)

= 2^(2+8)

= 2^10

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