Question

Find the missing value of six to the -3rd power times six to the? Power equals six to the 15th power what is the?

Answer 1

To solve for the missing exponent in the equation \(6^{-3} \times 6^x = 6^{15}\), we can use the property of exponents that states \(a^m \times a^n = a^{m+n}\).

Applying this property to our equation, we have:

\[
6^{-3 + x} = 6^{15}
\]

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

\[
-3 + x = 15
\]

Now, we can solve for \(x\) by adding 3 to both sides:

\[
x = 15 + 3
\]
\[
x = 18
\]

Thus, the missing value is \(18\).