What is the quotient -8a^8.b^{-2}/10a^{-4}.b^{-10 } in simplified form? Assume a≠ 0, b≠0

What is the quotient -8a^8.b^{-2}/10a^{-4}.b^{-10 } in simplified form? Assume a≠ 0, b≠0

What is the quotient -8a^8 b^{-2} / 10a^{-4} b^{-10} in simplified form? Assume a≠0, b≠0

To simplify the expression -8a^8 b^{-2} / 10a^{-4} b^{-10}, we can do this in several steps.

1. Separate the Constant Coefficients:

The coefficient part is (-8 / 10).

2. Simplify the Constant Coefficients:

\frac{-8}{10} = -\frac{4}{5}

3. Simplify the a Terms Using the Quotient Rule:

Next, apply the rules of exponents to the a terms. Recall that when dividing like bases, subtract the exponents:

a^{8 - (-4)} = a^{8 + 4} = a^{12}

4. Simplify the b Terms Using the Quotient Rule:

Do the same for the b terms:

b^{-2 - (-10)} = b^{-2 + 10} = b^8

5. Combine All Parts:

Putting it all together, we get:

-\frac{4}{5} a^{12} b^8

Final Simplified Form:

Therefore:

\boxed{-\frac{4}{5} a^{12} b^8}
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