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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].
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].
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