using a calculator, estimate the value of 32^1.4

Question

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Answer 1

To estimate ${32}^{1.4}$, you can break it down into more manageable parts.

1. Express 32 as a power of 2:
   $32=2^5$

2. Rewrite the expression:
   ${32}^{1.4}=(2^5{)}^{1.4}=2^{5\times 1.4}=2^7$

3. Calculate $2^7$:
   $2^7=128$

To refine the estimate since we have ${32}^{1.4}$ instead of ${32}^{1.0}$ or ${32}^{1.5}$, we can calculate ${32}^{1.4}$ more directly:

You can use a calculator for ${32}^{1.4}$, which gives approximately:
$${32}^{1.4}\approx 86.736$$

So the estimated value of ${32}^{1.4}$ is approximately 86.74.