QuestionApril 14, 2026

What is the quotient (-8a^8b^-2)/(10a^-4)b^(-10) in simplified form? Assume aneq 0,bneq 0

What is the quotient (-8a^8b^-2)/(10a^-4)b^(-10) in simplified form? Assume aneq 0,bneq 0
What is the quotient (-8a^8b^-2)/(10a^-4)b^(-10) in simplified form? Assume
aneq 0,bneq 0

Solution
4.7(250 votes)

Answer

-\frac{4}{5}a^{12}b^{8} Explanation 1. Simplify coefficients \frac{-8}{10} = -\frac{4}{5} 2. Simplify powers of a Use **a^m / a^n = a^{m-n}**: a^{8 - (-4)} = a^{8+4} = a^{12} 3. Simplify powers of b b^{-2 - (-10)} = b^{-2 + 10} = b^{8} 4. Combine results Multiply simplified coefficient, a term, and b term.

Explanation

1. Simplify coefficients <br /> $ \frac{-8}{10} = -\frac{4}{5} $ <br /><br />2. Simplify powers of $a$ <br /> Use **$a^m / a^n = a^{m-n}$**: $a^{8 - (-4)} = a^{8+4} = a^{12}$ <br /><br />3. Simplify powers of $b$ <br /> $b^{-2 - (-10)} = b^{-2 + 10} = b^{8}$ <br /><br />4. Combine results <br /> Multiply simplified coefficient, $a$ term, and $b$ term.
Click to rate: