Question

Simplify: (√36a¹0b² div 6a⁵b⁵)

(A) (6ab⁵)
(B) (6a⁵b)
(C) (6a⁵b⁵)
(D) None of the above options.

Answer 1

The simplified expression is (b⁵) / a⁴.

Step-by-step explanation:

To simplify the given expression (√36a¹⁰b² ÷ 6a⁵b⁵), we break down each term:

1. The square root of 36 is 6.

2. For the variables, we subtract the exponents in the numerator from the exponents in the denominator:

- a¹⁰ / a⁵ = a⁵

- b² / b⁵ = 1/b³ (subtracting exponents means dividing the terms)

Combining these results, we get (6 * a⁵) / (6 * b³), and the common factor of 6 cancels out:

`\[ ((6 \cdot a^5))/((6 \cdot b^3)) = (a^5)/(b^3) \]`

This simplification is equivalent to (b⁵) / a⁴, which is the final answer.

The use of subscript/superscript style helps represent exponents and variables clearly, allowing for a concise and accurate mathematical expression.