Exponent Rules Unit Test

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Question
What is the missing number in this simplified exponential expression: 7?÷75=712
?(1 point)

1 answer

To find the missing number in the expression \( 7^? \div 7^5 = 7^{12} \), we can use the quotient rule of exponents, which states that:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Applying this to the given equation:

\[ 7^? \div 7^5 = 7^{? - 5} \]

Setting that equal to \( 7^{12} \), we have:

\[ 7^{? - 5} = 7^{12} \]

Since the bases are the same, we can set the exponents equal to each other:

\[ ? - 5 = 12 \]

Now, solve for \( ? \):

\[ ? = 12 + 5 = 17 \]

Thus, the missing number is \( 17 \).