High School

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Apply the exponent properties to simplify the given expression.

[tex]\left(-4 x^7\right) \cdot\left(8 x^2\right)[/tex]

A. [tex]-32 x^9[/tex]
B. [tex]4 x^9[/tex]
C. [tex]-32 x^{14}[/tex]
D. [tex]4 x^{14}[/tex]

Answer :

Sure! Let's simplify the expression [tex]\((-4x^7) \cdot (8x^2)\)[/tex] step-by-step:

1. Multiply the Coefficients:
- You have two numbers multiplying here: [tex]\(-4\)[/tex] and [tex]\(8\)[/tex].
- Multiply these numbers: [tex]\(-4 \times 8 = -32\)[/tex].

2. Apply the Exponent Rule:
- For the [tex]\(x\)[/tex] values, you use the property of exponents: when you multiply two powers with the same base, you add the exponents.
- Here, you have [tex]\(x^7\)[/tex] and [tex]\(x^2\)[/tex].
- Add the exponents together: [tex]\(7 + 2 = 9\)[/tex].

3. Combine the Results:
- Put it all together with the coefficient and the exponent: [tex]\(-32x^9\)[/tex].

So, the simplified expression is [tex]\(-32x^9\)[/tex].

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