To simplify the expression [tex]\(\frac{y^6}{y^2}\)[/tex], we can use the properties of exponents. When you divide exponents with the same base, you can subtract the exponent in the denominator from the exponent in the numerator. Here's a step-by-step explanation:
1. Identify the base and the exponents:
- The base is [tex]\(y\)[/tex].
- The exponent in the numerator is [tex]\(6\)[/tex].
- The exponent in the denominator is [tex]\(2\)[/tex].
2. Apply the exponent subtraction property:
- According to the property of exponents, [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex], where [tex]\(a\)[/tex] is the base and [tex]\(m\)[/tex] and [tex]\(n\)[/tex] are the exponents.
- Here, [tex]\(a = y\)[/tex], [tex]\(m = 6\)[/tex], and [tex]\(n = 2\)[/tex].
3. Subtract the exponents:
- Subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
y^{6-2}
\][/tex]
4. Simplify the expression:
- Perform the subtraction:
[tex]\[
6 - 2 = 4
\][/tex]
5. Write the final simplified form:
- The expression simplifies to:
[tex]\[
y^4
\][/tex]
So, the simplified form of [tex]\(\frac{y^6}{y^2}\)[/tex] is [tex]\(y^4\)[/tex].
