find the miss value for z^?/z^6 = z^19

?=

1 answer

To solve for the missing exponent represented by the question mark (\(?\)) in the equation

\[ \frac{z^?}{z^6} = z^{19} \]

we can use the properties of exponents. When dividing two expressions with the same base, we subtract the exponent in the denominator from the exponent in the numerator:

\[ \frac{z^?}{z^6} = z^{? - 6} \]

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

\[ z^{? - 6} = z^{19} \]

Since the bases are the same, we can equate the exponents:

\[ ? - 6 = 19 \]

To isolate \(?\), we can add 6 to both sides:

\[ ? = 19 + 6 \]

So,

\[ ? = 25 \]

Therefore, the missing value for \( z^? \) is \( 25 \).