Question
Find the missing value for
x19x?=x5\frac{x^{19}}{x^?}=x^{5}
x
?
x
19
=x
5
Answers
GPT-4o mini
To solve the equation
\[
\frac{x^{19}}{x^{?}} = x^{5},
\]
we can use the properties of exponents. Specifically, we know that
\[
\frac{x^a}{x^b} = x^{a-b}.
\]
Applying this to the left-hand side, we have:
\[
\frac{x^{19}}{x^{?}} = x^{19 - ?}.
\]
Now, we can set the left-hand side equal to the right-hand side:
\[
x^{19 - ?} = x^{5}.
\]
Since the bases are the same, we can equate the exponents:
\[
19 - ? = 5.
\]
To find the value of \( ? \), we can rearrange the equation:
\[
? = 19 - 5.
\]
Calculating this gives us:
\[
? = 14.
\]
Thus, the missing value is
\[
\boxed{14}.
\]
\[
\frac{x^{19}}{x^{?}} = x^{5},
\]
we can use the properties of exponents. Specifically, we know that
\[
\frac{x^a}{x^b} = x^{a-b}.
\]
Applying this to the left-hand side, we have:
\[
\frac{x^{19}}{x^{?}} = x^{19 - ?}.
\]
Now, we can set the left-hand side equal to the right-hand side:
\[
x^{19 - ?} = x^{5}.
\]
Since the bases are the same, we can equate the exponents:
\[
19 - ? = 5.
\]
To find the value of \( ? \), we can rearrange the equation:
\[
? = 19 - 5.
\]
Calculating this gives us:
\[
? = 14.
\]
Thus, the missing value is
\[
\boxed{14}.
\]