Question

Find the missing number in this simplified exponential expression: 15 superscript ?÷15 superscript 7=15 superscript 12
.(1 point)
Responses

−5
negative 5

−19
negative 19

19
19

5

Answer 1

To solve for the missing exponent in the expression \( 15^{?} \div 15^{7} = 15^{12} \), we can use the property of exponents that states:

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

Using this property, we can rewrite the left side of the equation:

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

Now, we can set this equal to the right side of the equation:

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

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

\[
? - 7 = 12
\]

To find \( ? \), we solve the equation:

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

Thus, the missing number is \( \boxed{19} \).