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Answer :
Sure, let's break it down step-by-step for each part of the question.
Part 3: Simplifying [tex]\( x^5 \cdot x^9 \)[/tex]
1. When you multiply expressions with the same base, you add the exponents. This is because of the rule of exponents: [tex]\( x^a \cdot x^b = x^{a+b} \)[/tex].
2. Here, both expressions are powers of [tex]\( x \)[/tex], so we have:
[tex]\[
x^5 \cdot x^9 = x^{5+9}
\][/tex]
3. Simplifying the exponent, you get:
[tex]\[
x^{14}
\][/tex]
So, the product of [tex]\( x^5 \cdot x^9 \)[/tex] is [tex]\( x^{14} \)[/tex].
Part 4: Simplifying [tex]\( (6x^2)(4x^2) \)[/tex]
1. When multiplying expressions of the form [tex]\( (ax^b) \cdot (cx^d) \)[/tex], you multiply the coefficients (numbers in front of [tex]\( x \)[/tex]) and add the exponents of [tex]\( x \)[/tex].
2. For this expression:
- Multiply the coefficients: [tex]\( 6 \cdot 4 = 24 \)[/tex].
- Add the exponents of [tex]\( x \)[/tex] (both are 2): [tex]\( 2 + 2 = 4 \)[/tex].
3. This gives you:
[tex]\[
24x^4
\][/tex]
Therefore, the product of [tex]\( (6x^2)(4x^2) \)[/tex] is [tex]\( 24x^4 \)[/tex].
In summary:
- The product [tex]\( x^5 \cdot x^9 = x^{14} \)[/tex].
- The product [tex]\( (6x^2)(4x^2) = 24x^4 \)[/tex].
Part 3: Simplifying [tex]\( x^5 \cdot x^9 \)[/tex]
1. When you multiply expressions with the same base, you add the exponents. This is because of the rule of exponents: [tex]\( x^a \cdot x^b = x^{a+b} \)[/tex].
2. Here, both expressions are powers of [tex]\( x \)[/tex], so we have:
[tex]\[
x^5 \cdot x^9 = x^{5+9}
\][/tex]
3. Simplifying the exponent, you get:
[tex]\[
x^{14}
\][/tex]
So, the product of [tex]\( x^5 \cdot x^9 \)[/tex] is [tex]\( x^{14} \)[/tex].
Part 4: Simplifying [tex]\( (6x^2)(4x^2) \)[/tex]
1. When multiplying expressions of the form [tex]\( (ax^b) \cdot (cx^d) \)[/tex], you multiply the coefficients (numbers in front of [tex]\( x \)[/tex]) and add the exponents of [tex]\( x \)[/tex].
2. For this expression:
- Multiply the coefficients: [tex]\( 6 \cdot 4 = 24 \)[/tex].
- Add the exponents of [tex]\( x \)[/tex] (both are 2): [tex]\( 2 + 2 = 4 \)[/tex].
3. This gives you:
[tex]\[
24x^4
\][/tex]
Therefore, the product of [tex]\( (6x^2)(4x^2) \)[/tex] is [tex]\( 24x^4 \)[/tex].
In summary:
- The product [tex]\( x^5 \cdot x^9 = x^{14} \)[/tex].
- The product [tex]\( (6x^2)(4x^2) = 24x^4 \)[/tex].
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