Question

What is the simplest form of x.y⁶. x⁹.y⁹ .

Answer 1

The expression x.y⁶ . x⁹.y⁹ simplifies to x¹⁰.yⁱ⁵ by adding the exponents of like bases, which in this case are x and y.

Step-by-step explanation:

The student is asking for help to simplify the expression x.y⁶ . x⁹.y⁹. When simplifying expressions with exponents, we use the rule that when multiplying two powers with the same base, we can simply add the exponents. So, for the expression x.y⁶ . x⁹.y⁹, we add the exponents for x and y separately.

For the x terms, we have x¹ (which is just x) and x⁹, so applying the rule x^(p+q) = x¹ * x⁹, we add the exponents directly:

• 1 (from x¹) + 9 (from x⁹) = 10, so that gives us x¹⁰.

For the y terms, we have y⁶ and y⁹. Applying the same rule, we add the exponents:

• 6 (from y⁶) + 9 (from y⁹) = 15, giving us yⁱ⁵.

Therefore, the expression x.y⁶ . x⁹.y⁹ simplifies to x¹⁰.yⁱ⁵.