To simplify the expression [tex]\(\frac{a^{10}}{a^5} \cdot -\frac{1}{3}\)[/tex], follow these steps:
1. Simplify the fraction [tex]\(\frac{a^{10}}{a^5}\)[/tex]:
- When dividing exponents with the same base, subtract the exponent in the denominator from the exponent in the numerator.
- So, [tex]\(\frac{a^{10}}{a^5}\)[/tex] becomes [tex]\(a^{10-5}\)[/tex].
2. Perform the exponent subtraction:
- [tex]\(10 - 5 = 5\)[/tex]
- Therefore, [tex]\(\frac{a^{10}}{a^5} = a^5\)[/tex].
3. Multiply the simplified expression by [tex]\(-\frac{1}{3}\)[/tex]:
- Now multiply [tex]\(a^5\)[/tex] by [tex]\(-\frac{1}{3}\)[/tex].
- This can be written as [tex]\(a^5 \cdot -\frac{1}{3}\)[/tex].
Putting it all together, the simplification process leads to:
[tex]\[
\frac{a^{10}}{a^5} \cdot -\frac{1}{3} = a^5 \cdot -\frac{1}{3}
\][/tex]
Thus, the simplified form of the expression is:
[tex]\[
a^5 \cdot -\frac{1}{3}
\][/tex]
