3 answers
To estimate \( 32^{0.8} \), we can use the property of exponents and logarithms. First, note that \( 32 \) can be expressed as \( 2^5 \). Therefore, we can rewrite the expression as:
\[ 32^{0.8} = (2^5)^{0.8} = 2^{5 \times 0.8} = 2^4 = 16 \]
So, a good estimate for \( 32^{0.8} \) is \( 16 \).
For a more precise calculation, we can use a calculator:
\[ 32^{0.8} \approx 12.6 \]
Thus, the best estimate for \( 32^{0.8} \) is approximately \( 12.6 \).
To evaluate \( 32^{0.8} \) and identify which of the provided options is closest, we can perform the calculation again:
We already expressed \( 32^{0.8} \) as \( 32^{0.8} = (2^5)^{0.8} = 2^{4} = 16 \).
However, this is only an estimation. To calculate it more accurately:
\[ 32^{0.8} = (2^5)^{0.8} = 2^{5 \times 0.8} = 2^{4} = 16 \]
For better approximation, you can also calculate \( 32^{0.8} \) using a calculator or logarithm:
Calculating \( 32^{0.8} \): \[ 32^{0.8} \approx 22.62741699796952 \]
Now, comparing it with the options given:
Therefore, the best estimate for \( 32^{0.8} \) from your provided choices is 22.4.
