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What is the product?

[tex]\[ \left(7 x^2 y^3\right)\left(3 x^5 y^8\right) \][/tex]

A. [tex]\( 10 x^7 y^{11} \)[/tex]

B. [tex]\( 10 x^{10} y^{24} \)[/tex]

C. [tex]\( 21 x^7 y^{11} \)[/tex]

D. [tex]\( 21 x^{10} y^{24} \)[/tex]


Sagot :

To find the product of the two given expressions [tex]\(\left(7 x^2 y^3\right)\left(3 x^5 y^8\right)\)[/tex], follow these steps:

1. Multiply the coefficients:
- The coefficients are 7 and 3.
- When we multiply these coefficients together, we get [tex]\(7 \times 3 = 21\)[/tex].

2. Combine the powers of [tex]\(x\)[/tex]:
- In the first term [tex]\(7 x^2 y^3\)[/tex], the power of [tex]\(x\)[/tex] is 2.
- In the second term [tex]\(3 x^5 y^8\)[/tex], the power of [tex]\(x\)[/tex] is 5.
- When you multiply terms with the same base, you add their exponents: [tex]\(x^2 \times x^5 = x^{2+5} = x^7\)[/tex].

3. Combine the powers of [tex]\(y\)[/tex]:
- In the first term [tex]\(7 x^2 y^3\)[/tex], the power of [tex]\(y\)[/tex] is 3.
- In the second term [tex]\(3 x^5 y^8\)[/tex], the power of [tex]\(y\)[/tex] is 8.
- Similarly, when you multiply terms with the same base, you add their exponents: [tex]\(y^3 \times y^8 = y^{3+8} = y^{11}\)[/tex].

Putting it all together, the product of [tex]\(\left(7 x^2 y^3\right)\left(3 x^5 y^8\right)\)[/tex] is:
[tex]\[ 21 x^7 y^{11} \][/tex]

Therefore, the correct answer is:
[tex]\[ 21 x^7 y^{11} \][/tex]
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