Question

(ab)^10:(a^9*b^8)*a^2​

Answer 1

$(ab)^{10}:(a^9*b^8)*a^2=a^{10}b^{10}:a^{11}b^8=a^{10-11}b^{10-8}=a^{-1}b^2=\frac{b^2}{a}$

Answer 2

To simplify the given expression, let's break down each term step by step:

1. (ab)^10: This means raising the product of a and b to the power of 10. So, (ab)^10 = a^10 * b^10.

2. (a^9 * b^8) * a^2: Here, you're multiplying a^9 * b^8 and then multiplying the result by a^2. When you multiply like bases with the same exponent, you add their exponents. So, a^9 * a^2 = a^(9+2) = a^11, and b^8 remains the same.

Now, let's simplify the expression:

cssCopy code
(a^10 * b^10) / (a^11 * b^8)

When you're dividing like bases with the same exponent, you subtract the exponents in the denominator from the exponents in the numerator. So, a^10 / a^11 = a^(10-11) = a^(-1), and b^10 / b^8 = b^(10-8) = b^2.

Putting it all together:

cssCopy code
(a^(-1) * b^2)

Thus, the simplified expression is:

cssCopy code
b^2 / a

Keep in mind that negative exponents in the final result indicate division by the corresponding positive exponent term.