College

Simplify this expression. Assume that x is nonzero.

[tex]x^{-9} \cdot x^4[/tex]

[tex]x^{-9} \cdot x^4 = \square[/tex]

(Type exponential notation with positive exponents.)

Answer :

To simplify the expression [tex]\( x^{-9} \cdot x^4 \)[/tex], you need to apply the properties of exponents. Here's a step-by-step explanation:

1. Understand the Exponent Rule: The property of exponents states that when you multiply two powers with the same base, you add their exponents. In general, [tex]\( a^m \cdot a^n = a^{m+n} \)[/tex].

2. Apply the Rule to the Expression: In this problem, you're working with [tex]\( x^{-9} \cdot x^4 \)[/tex]. According to the rule, you add the exponents:
[tex]\[
-9 + 4 = -5
\][/tex]
So, the expression becomes [tex]\( x^{-5} \)[/tex].

3. Express with Positive Exponent: To express the result with a positive exponent, use the property that [tex]\( a^{-m} = \frac{1}{a^m} \)[/tex]. Therefore,
[tex]\[
x^{-5} = \frac{1}{x^5}
\][/tex]
This is the simplified form of the expression using positive exponents.

Thus, the simplified expression in exponential notation with a positive exponent is [tex]\(\frac{1}{x^5}\)[/tex].