Question

which of the following expressions is equivalent to 9 + 9·49?
$3^2 + 7·3^2$
$3^2 + 7^3·3^2$
$3^2 + 7^2·3$
$3^2 + 7^2·3^2$
skill code: 104300

Explanation:

Step1: Simplify original expression

First, note that \(9 = 3^2\) and \(49 = 7^2\). So the original expression \(9 + 9\times49\) can be rewritten as \(3^2+3^2\times7^2\) (since \(9\times49 = 3^2\times7^2\)). Wait, let's check each option:

Wait, let's re - express the original expression: \(9+9\times49=9(1 + 49)=9\times50\), but let's use exponent rules. \(9 = 3^2\), \(49=7^2\), so \(9 + 9\times49=3^2+3^2\times7^2\).

Now let's check each option:

Option 1: \(3^2+7\times3^2=3^2(1 + 7)=3^2\times8
eq3^2+3^2\times7^2\)

Option 2: \(3^2+7^3\times3^2=3^2(1 + 343)=3^2\times344
eq3^2+3^2\times7^2\)

Option 3: \(3^2+7^2\times3=9 + 49\times3=9 + 147 = 156\), original expression: \(9+9\times49=9+441 = 450\), not equal.

Option 4: \(3^2+7^2\times3^2=9+49\times9=9(1 + 49)=9\times50 = 450\), which is equal to the original expression \(9 + 9\times49=9+441 = 450\)

Answer:

\(3^{2}+7^{2}\cdot3^{2}\) (the fourth option)