Questions: (7a/4)^3

Solution Steps

To solve the expression \(\left(\frac{7a}{4}\right)^{3}\), we need to raise the fraction \(\frac{7a}{4}\) to the power of 3. This involves raising both the numerator and the denominator to the power of 3 separately.

We start with the expression \(\left(\frac{7a}{4}\right)^{3}\). To evaluate this, we substitute \(a = 1\):

\[ \left(\frac{7 \cdot 1}{4}\right)^{3} = \left(\frac{7}{4}\right)^{3} \]

Next, we calculate the numerator and denominator separately:

\[ \text{Numerator: } 7^{3} = 343 \] \[ \text{Denominator: } 4^{3} = 64 \]

Now we can form the final fraction:

\[ \left(\frac{7}{4}\right)^{3} = \frac{343}{64} \]

To express this as a decimal, we perform the division:

\[ \frac{343}{64} \approx 5.359375 \]

Final Answer