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Answer :
Sure! Let's simplify the given exponential expression [tex]\( x^9 \cdot x^4 \)[/tex] step-by-step.
1. Identify the exponents and the base:
- We have the same base [tex]\( x \)[/tex] in both terms.
- The exponents are 9 and 4 respectively.
2. Use the properties of exponents:
- According to the property of exponents, when you multiply two exponential expressions with the same base, you add the exponents:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
- In this case, [tex]\( a = x \)[/tex], [tex]\( m = 9 \)[/tex], and [tex]\( n = 4 \)[/tex].
3. Add the exponents:
- Combine the exponents together:
[tex]\[ 9 + 4 = 13 \][/tex]
4. Write the simplified expression:
- Now, the expression [tex]\( x^9 \cdot x^4 \)[/tex] simplifies to:
[tex]\[ x^{13} \][/tex]
So, the simplified expression is:
[tex]\[ x^9 \cdot x^4 = x^{13} \][/tex]
1. Identify the exponents and the base:
- We have the same base [tex]\( x \)[/tex] in both terms.
- The exponents are 9 and 4 respectively.
2. Use the properties of exponents:
- According to the property of exponents, when you multiply two exponential expressions with the same base, you add the exponents:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
- In this case, [tex]\( a = x \)[/tex], [tex]\( m = 9 \)[/tex], and [tex]\( n = 4 \)[/tex].
3. Add the exponents:
- Combine the exponents together:
[tex]\[ 9 + 4 = 13 \][/tex]
4. Write the simplified expression:
- Now, the expression [tex]\( x^9 \cdot x^4 \)[/tex] simplifies to:
[tex]\[ x^{13} \][/tex]
So, the simplified expression is:
[tex]\[ x^9 \cdot x^4 = x^{13} \][/tex]
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