Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

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

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• 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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• 4 × 16^2

= 2^2 × 2^8

= 2^10

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• 4 × 16^2

= 2^2 × 2^8

= 2^10

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• 4 * 16^2 =

2^2 * 4^2 =

2^(2 + 4) =

2^6

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• 1024 = 2^10.

Many ways to arrive at this...

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• :-

2^2 x 4^4 = 2^2 x 2^8 = 2^10

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• 4 x 16² =

2² x (2⁴)² =

2² x 2⁸ =

2²⁺⁸ =

2¹⁰...........ANS

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• 2 x 2 x (2 x 2 x 2 x 2 ) x ( 2 x 2 x 2 x 2)

= 2^10

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• 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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• 4 * 16^2 = (2^2) * (2^4)^2 = (2^2) * (2^8) = 2^10

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