Question

Simplify the following expression to simplest form using only positive

exponents.
(81x^-16 y^-28)^1/4

Answer 1

To simplify the expression (81x^-16 y^-28)^1/4 to the simplest form using only positive exponents, we can apply the rules of exponents.

Let's break down the steps:

Step 1: Distribute the exponent to each term inside the parentheses:

(81^(1/4) * x^(-16/4) * y^(-28/4))

Step 2: Simplify each term:

(3 * x^(-4) * y^(-7))

Step 3: Rewrite negative exponents as positive exponents:

(3 / x^4 * 1 / y^7)

Step 4: Combine the terms:

3 / (x^4 * y^7)

In summary, the simplified form of the expression (81x^-16 y^-28)^1/4, using only positive exponents, is 3 / (x^4 * y^7).

Answer 2

Answer: x3+y3+z3=k

Step-by-step explanation:

x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."

When there are two or more unknowns, as is the case here, only the integers are studied. The trick is finding integers that work for all equations, or the numbers for x, y, and z that will all equal k. Over the years, scientists have solved for nearly every integer between 0 and 100. The last two that remained were 33 and 42.