What is the missing number in this simplified exponential expression: 7?÷75=712

?(1 point)

1 answer

Let's solve the equation step by step.

You have:

\[ 7? \div 75 = 712 \]

To find \(7?\), you can multiply both sides of the equation by 75:

\[ 7? = 712 \times 75 \]

Now, calculate \(712 \times 75\):

\[ 712 \times 75 = 53400 \]

So now we have:

\[ 7? = 53400 \]

To find the digit represented by '?', we can express \(53400\) in the form \(7?\):

This means \(7?\) should represent \(53400\). Hence, the missing digit '?' to form \(53400\) is the digit in the tens place.

We see \(53400\) can be formed as:

\[ 7 = 5\text{ (thousand)} + 3\text{ (hundred)} + 4\text{ (ten)} + 0\text{ (unit)}\]

So we want the missing digit, which is:

\[ 70 \to 7 \text{ (in thousands)} + 0\]

Hence, the digit '?' represents \(0\).

Therefore, the answer is:

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