Bradley Schmidt
01/18/2024 · Middle School
FMU Question 3 Use the exponent rules to calculate the value of \( \left(\frac{144}{9}\right)^{\frac{1}{2}} \) (without calculator)
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Tutor-Verified Answer
Step-by-step Solution
To calculate \( \left(\frac{144}{9}\right)^{\frac{1}{2}} \), we can start by simplifying the fraction inside the parentheses.
First, we simplify \( \frac{144}{9} \):
\[
\frac{144}{9} = 16
\]
Now we can rewrite the expression:
\[
\left(\frac{144}{9}\right)^{\frac{1}{2}} = 16^{\frac{1}{2}}
\]
Next, we apply the exponent rule for square roots. The expression \( 16^{\frac{1}{2}} \) represents the square root of 16:
\[
16^{\frac{1}{2}} = \sqrt{16}
\]
Since \( \sqrt{16} = 4 \), we find that:
\[
\left(\frac{144}{9}\right)^{\frac{1}{2}} = 4
\]
Thus, the final answer is:
\[
\boxed{4}
\]
Quick Answer
The value of \( \left(\frac{144}{9}\right)^{\frac{1}{2}} \) is 4.
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