To simplify [tex]\(\frac{y^{-6}}{y^{-7}}\)[/tex] and express the answer with a positive exponent, follow these steps:
1. Apply the properties of exponents:
The quotient rule for exponents states that [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]. Here, we can apply this rule to our expression.
[tex]\[
\frac{y^{-6}}{y^{-7}} = y^{-6 - (-7)}
\][/tex]
2. Simplify the exponent:
Subtract the exponents in the numerator and the denominator.
[tex]\[
-6 - (-7) = -6 + 7 = 1
\][/tex]
3. Rewrite the expression:
Now replace the exponent with the simplified result.
[tex]\[
y^{1}
\][/tex]
4. Final result:
The simplified form of the expression with a positive exponent is:
[tex]\[
y
\][/tex]
Thus, the expression [tex]\(\frac{y^{-6}}{y^{-7}}\)[/tex] simplifies to [tex]\(y\)[/tex].
