Question

simplify.
\\(dfrac{x^3}{x^7}\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we use the rule \( \frac{a^m}{a^n}=a^{m - n} \), where \( a
eq0 \), \( m \) and \( n \) are real numbers. Here, the base \( a = x \), \( m = 3 \), and \( n = 7 \).

Step2: Apply the exponent rule

Substitute the values into the rule: \( \frac{x^3}{x^7}=x^{3 - 7} \)

Step3: Simplify the exponent

Calculate \( 3-7=-4 \), so we get \( x^{-4} \). We can also express this using the rule \( a^{-n}=\frac{1}{a^n} \) as \( \frac{1}{x^4} \).

Answer:

\( \frac{1}{x^4} \) (or \( x^{-4} \))