Question
Evaluate: \( \frac{4}{7}\left(\frac{1}{4}\right)^{2} \)
Ask by Paul Kirk. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{1}{28}
\]
Solution
To evaluate the expression:
\[
\frac{4}{7}\left(\frac{1}{4}\right)^{2}
\]
follow these steps:
1. **Calculate the Exponentiation:**
First, evaluate \(\left(\frac{1}{4}\right)^{2}\):
\[
\left(\frac{1}{4}\right)^{2} = \frac{1^2}{4^2} = \frac{1}{16}
\]
2. **Multiply the Fractions:**
Now, multiply \(\frac{4}{7}\) by \(\frac{1}{16}\):
\[
\frac{4}{7} \times \frac{1}{16} = \frac{4 \times 1}{7 \times 16} = \frac{4}{112}
\]
3. **Simplify the Fraction:**
Simplify \(\frac{4}{112}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[
\frac{4 \div 4}{112 \div 4} = \frac{1}{28}
\]
**Final Answer:**
\[
\frac{4}{7}\left(\frac{1}{4}\right)^{2} = \frac{1}{28}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
Let's solve the expression step by step. First, evaluate \( \left(\frac{1}{4}\right)^{2} \): \[ \left(\frac{1}{4}\right)^{2} = \frac{1^{2}}{4^{2}} = \frac{1}{16} \] Next, substitute this back into the original expression: \[ \frac{4}{7} \left(\frac{1}{4}\right)^{2} = \frac{4}{7} \cdot \frac{1}{16} \] Now, multiply the fractions: \[ \frac{4 \cdot 1}{7 \cdot 16} = \frac{4}{112} \] Then, simplify \( \frac{4}{112} \): \[ \frac{4 \div 4}{112 \div 4} = \frac{1}{28} \] Therefore, the final answer is: \[ \boxed{\frac{1}{28}} \]
