Find the missing number in this simplified exponential expression: 15^?÷15^7=15^12

Question

.(1 point)
Responses

19

−5

−19

5

Answer 1

To simplify the expression \( 15^? \div 15^7 = 15^{12} \), you can use the property of exponents:

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

Applying this property here gives:

\[ 15^? \div 15^7 = 15^{? - 7} \]

So we can rewrite the equation as:

\[ 15^{? - 7} = 15^{12} \]

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

\[ ? - 7 = 12 \]

Now, solve for \( ? \):

\[ ? = 12 + 7 = 19 \]

Thus, the missing number is \( 19 \).

The answer is \( \boxed{19} \).