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].
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].
