What is the missing number in this simplified exponential expression: (7 ^ 2) / (7 ^ 5) =7^ 12?

1 answer

To simplify the expression \((7^2) / (7^5)\), we can use the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\).

Applying this property:

\[ \frac{7^2}{7^5} = 7^{2-5} = 7^{-3} \]

Thus, \((7^2) / (7^5) = 7^{-3}\), not \(7^{12}\).

So, we conclude that the equation you're considering is incorrect, and the simplified expression results in \(7^{-3}\). Hence, there is no missing number to make \((7^2) / (7^5) = 7^{12}\) true.

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