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

Question

.(1 point)
Responses

19
19

−19
negative 19

5
5

−5

Answer 1

To solve the equation \( \frac{15^?}{15^7} = 15^{12} \), we can use the properties of exponents.

Using the quotient rule of exponents, we have:

\[ \frac{15^a}{15^b} = 15^{a-b} \]

So, applying that to our equation:

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

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

\[ ? - 7 = 12 \]

Now, we can solve for \( ? \):

\[ ? = 12 + 7 \] \[ ? = 19 \]

Therefore, the missing number is:

19