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.