Answer :
To simplify the expression [tex]\( x^{-9} \cdot x^4 \)[/tex], we can use the properties of exponents.
When you multiply terms with the same base, you add their exponents. The rule is:
[tex]\[ x^a \cdot x^b = x^{a+b} \][/tex]
Now, let's apply this rule to our expression:
1. Identify the exponents:
- The exponent of the first term [tex]\( x^{-9} \)[/tex] is [tex]\(-9\)[/tex].
- The exponent of the second term [tex]\( x^4 \)[/tex] is [tex]\(4\)[/tex].
2. Add the exponents together:
[tex]\(-9 + 4 = -5\)[/tex].
3. Write the simplified expression using the new exponent:
[tex]\[ x^{-5} \][/tex]
So, the simplified form of [tex]\( x^{-9} \cdot x^4 \)[/tex] is [tex]\( x^{-5} \)[/tex].
When you multiply terms with the same base, you add their exponents. The rule is:
[tex]\[ x^a \cdot x^b = x^{a+b} \][/tex]
Now, let's apply this rule to our expression:
1. Identify the exponents:
- The exponent of the first term [tex]\( x^{-9} \)[/tex] is [tex]\(-9\)[/tex].
- The exponent of the second term [tex]\( x^4 \)[/tex] is [tex]\(4\)[/tex].
2. Add the exponents together:
[tex]\(-9 + 4 = -5\)[/tex].
3. Write the simplified expression using the new exponent:
[tex]\[ x^{-5} \][/tex]
So, the simplified form of [tex]\( x^{-9} \cdot x^4 \)[/tex] is [tex]\( x^{-5} \)[/tex].
