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Answer :
To solve the expression [tex]\(\frac{-8 x^6}{4 x^{-3}}\)[/tex], follow these steps:
1. Simplify the coefficients:
[tex]\[
\frac{-8}{4} = -2
\][/tex]
2. Simplify the exponents:
When dividing like bases, subtract the exponents:
[tex]\[
\frac{x^6}{x^{-3}} = x^{6 - (-3)} = x^{6 + 3} = x^9
\][/tex]
3. Combine the simplified coefficient and exponent terms:
[tex]\[
\frac{-8 x^6}{4 x^{-3}} = -2 x^9
\][/tex]
So, the quotient of [tex]\(\frac{-8 x^6}{4 x^{-3}}\)[/tex] is [tex]\(-2 x^9\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{-2 x^9}
\][/tex]
1. Simplify the coefficients:
[tex]\[
\frac{-8}{4} = -2
\][/tex]
2. Simplify the exponents:
When dividing like bases, subtract the exponents:
[tex]\[
\frac{x^6}{x^{-3}} = x^{6 - (-3)} = x^{6 + 3} = x^9
\][/tex]
3. Combine the simplified coefficient and exponent terms:
[tex]\[
\frac{-8 x^6}{4 x^{-3}} = -2 x^9
\][/tex]
So, the quotient of [tex]\(\frac{-8 x^6}{4 x^{-3}}\)[/tex] is [tex]\(-2 x^9\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{-2 x^9}
\][/tex]
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