Questions: What is the value of the following expression? 49^2 / (3 * 7^3) (A) 7/3 (B) 3/7 (C) 1/7 (D) 1/21

Solution Steps

The numerator of the expression is \(49^2\). We know that \(49 = 7^2\), so:

\[ 49^2 = (7^2)^2 = 7^{4} \]

The denominator of the expression is \(3 \times 7^3\). This can be rewritten as:

\[ 3 \times 7^3 \]

Now, substitute the simplified forms of the numerator and the denominator into the expression:

\[ \frac{49^2}{3 \times 7^3} = \frac{7^4}{3 \times 7^3} \]

We can simplify this by canceling out \(7^3\) from the numerator and the denominator:

\[ = \frac{7^{4-3}}{3} = \frac{7}{3} \]

Final Answer