Question

Which expression has the greatest value?(options are included in the image)

Answer 1

Answer:

  (b)  16^(3/2)

Step-by-step explanation:

Your calculator is a good source of information about the values of numerical expressions.

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Here, all of the expressions have a value of 16 except 16^(3/2). That has the greatest value.

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Additional comment

Assuming you're familiar with powers of 2 and the rules of exponents, you can evaluate these without a calculator:

  ∛(64²) = ∛(2^6)² = (2^12)^(1/3) = 2^4

  16^(3/2) = (2^4)^(3/2) = 2^6 . . . . . has the greatest value

  √(16²) = ((2^4)^2)^(1/2) = 2^(4·2/2) = 2^4

  ∛(8^4) = ((2^3)^4)^(1/3) = 2^(3·4/3) = 2^4

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8= 2^3; 16 = 2^4; 64 = 2^6

(a^b)^c = a^(bc)

A root is equivalent to a fractional power. The cube root is the 1/3 power, for example.