To simplify the expression \(\frac{x^{-6}}{y^4}\), we can use the properties of exponents. Let’s go through this step-by-step:
1. Rewrite the expression using the negative exponent rule: When we have a negative exponent, \(a^{-n} = \frac{1}{a^n}\). So, we can rewrite \(x^{-6}\) using this rule:
[tex]\[
x^{-6} = \frac{1}{x^6}
\][/tex]
Now our expression becomes:
[tex]\[
\frac{\frac{1}{x^6}}{y^4}
\][/tex]
2. Combine the fractions: When you divide by a fraction, it's the same as multiplying by the reciprocal of that fraction. Thus,
[tex]\[
\frac{\frac{1}{x^6}}{y^4} = \frac{1}{x^6} \cdot \frac{1}{y^4}
\][/tex]
3. Multiply the fractions: To multiply fractions, you multiply the numerators together and the denominators together:
[tex]\[
\frac{1}{x^6} \cdot \frac{1}{y^4} = \frac{1 \cdot 1}{x^6 \cdot y^4} = \frac{1}{x^6 y^4}
\][/tex]
Thus, the simplified form of the expression \(\frac{x^{-6}}{y^4}\) is:
[tex]\[
\frac{1}{x^6 y^4}
\][/tex]
