Answer :
Sure! Let's break down the problem step-by-step using the properties of exponents.
We have the expression:
[tex]\[ x^9 \cdot x^{-4} \][/tex]
When you multiply expressions with the same base, you can add their exponents. This is a key property of exponents:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
In this case, the base is [tex]\(x\)[/tex], and the exponents are 9 and -4. Let's apply the property:
1. Identify the exponents: Here, [tex]\(m = 9\)[/tex] and [tex]\(n = -4\)[/tex].
2. Add the exponents:
[tex]\[ 9 + (-4) = 9 - 4 = 5 \][/tex]
3. Write the result with the new exponent:
Since we have added the exponents, the expression simplifies to:
[tex]\[ x^5 \][/tex]
So, the final result for the expression [tex]\( x^9 \cdot x^{-4} \)[/tex] is [tex]\( x^5 \)[/tex].
We have the expression:
[tex]\[ x^9 \cdot x^{-4} \][/tex]
When you multiply expressions with the same base, you can add their exponents. This is a key property of exponents:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
In this case, the base is [tex]\(x\)[/tex], and the exponents are 9 and -4. Let's apply the property:
1. Identify the exponents: Here, [tex]\(m = 9\)[/tex] and [tex]\(n = -4\)[/tex].
2. Add the exponents:
[tex]\[ 9 + (-4) = 9 - 4 = 5 \][/tex]
3. Write the result with the new exponent:
Since we have added the exponents, the expression simplifies to:
[tex]\[ x^5 \][/tex]
So, the final result for the expression [tex]\( x^9 \cdot x^{-4} \)[/tex] is [tex]\( x^5 \)[/tex].
