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

.(1 point)
Responses

5
5

−19
negative 19

−5
negative 5

19

1 answer

To solve the equation \( 15^? \div 15^7 = 15^{12} \), we can use the properties of exponents. Specifically, when dividing like bases, we subtract the exponents:

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

Setting this equal to \( 15^{12} \):

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

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 correct response is:

19