Answer :
Let's solve the problem step-by-step to understand who is right, Sandy or Terry.
The expression given is [tex]\((3x^2)(3x^5)\)[/tex].
### Step 1: Applying the Distributive Property
First, we handle the numerical coefficients and the powers of [tex]\(x\)[/tex] separately:
1. Numerical Coefficients:
Multiply the coefficients: [tex]\(3 \times 3 = 9\)[/tex].
2. Powers of [tex]\(x\)[/tex]:
Using the property of exponents, [tex]\((x^a)(x^b) = x^{a+b}\)[/tex], we add the exponents of [tex]\(x\)[/tex]:
[tex]\((x^2)(x^5) = x^{2+5} = x^7\)[/tex].
### Step 2: Combining the Results
Combine the results from step 1:
- The numerical part gives us 9.
- The powers of [tex]\(x\)[/tex] give us [tex]\(x^7\)[/tex].
Therefore, the expression [tex]\((3x^2)(3x^5)\)[/tex] simplifies to [tex]\(9x^7\)[/tex].
### Conclusion
Sandy claimed that [tex]\((3x^2)(3x^5) = 9x^7\)[/tex], which matches our result. Terry's answer of [tex]\(9x^{10}\)[/tex] is incorrect. Therefore, Sandy is right.
The expression given is [tex]\((3x^2)(3x^5)\)[/tex].
### Step 1: Applying the Distributive Property
First, we handle the numerical coefficients and the powers of [tex]\(x\)[/tex] separately:
1. Numerical Coefficients:
Multiply the coefficients: [tex]\(3 \times 3 = 9\)[/tex].
2. Powers of [tex]\(x\)[/tex]:
Using the property of exponents, [tex]\((x^a)(x^b) = x^{a+b}\)[/tex], we add the exponents of [tex]\(x\)[/tex]:
[tex]\((x^2)(x^5) = x^{2+5} = x^7\)[/tex].
### Step 2: Combining the Results
Combine the results from step 1:
- The numerical part gives us 9.
- The powers of [tex]\(x\)[/tex] give us [tex]\(x^7\)[/tex].
Therefore, the expression [tex]\((3x^2)(3x^5)\)[/tex] simplifies to [tex]\(9x^7\)[/tex].
### Conclusion
Sandy claimed that [tex]\((3x^2)(3x^5) = 9x^7\)[/tex], which matches our result. Terry's answer of [tex]\(9x^{10}\)[/tex] is incorrect. Therefore, Sandy is right.
