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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