prove that : 3^-3 * 6^2 * root 98 divided by 5 ^2 * cube root 1/25 * 15 ^-4/3 * 3^1/3 equals to 28 root 2

Apparently you totally ignored or did not even read my reply, since you typed it again exactly the same way

http://www.jiskha.com/display.cgi?id=1364632096

To prove that the given expression is equal to 28√2, we'll simplify both sides of the equation separately and then check if they are equal.

Let's start by simplifying the left side of the equation:

3^-3 * 6^2 * √98 / (5^2 * ∛(1/25) * 15^(-4/3) * ∛3)

First, let's simplify the exponents:

3^-3 = 1 / 3^3 = 1 / 27

6^2 = 6 * 6 = 36

∛98 = ∛(49 * 2) = ∛49 * ∛2 = 7√2

∛(1/25) = ∛(1) / ∛(25) = 1 / 5

15^(-4/3) = 1 / 15^(4/3) = 1 / (cubed root of 15^4)

∛3 = cube root of 3

Now let's substitute the new values into the expression:

(1 / 27) * 36 * (7√2) / (5^2 * (1/5) * (1 / cubed root of 15^4) * (cube root of 3))

Now, simplify the terms:

(1 / 27) * 36 * (7√2) = (36 * 7√2) / 27 = 252√2 / 27

(5^2 * (1/5)) = (25 * 1/5) = 5

1 / cubed root of 15^4 = 1 / (15^4)^(1/3) = 1 / (15^(4/3))

cube root of 3 = ∛3

Now substitute the new values into the expression again:

(252√2 / 27) * 5 / (1 / (15^(4/3))) * (∛3)

Simplify further:

(252√2 / 27) * 5 / (1 / (15^(4/3))) * (∛3) = (252√2 * 5 * 15^(4/3) * ∛3) / 27

Now, let's simplify the expression:

252 * 5 = 1260

√2 * √2 = 2

15^(4/3) = cube root of 15^4 = cube root of (15 * 15 * 15 * 15) = 15^3 = 15 * 15 * 15 = 3375

∛3 = cube root of 3

Now substitute all the simplified values into the expression:

(1260 * 2 * 3375 * cube root of 3) / 27

Simplify further:

(1260 * 2 * 3375 * cube root of 3) / 27 = 9072000 * cube root of 3 / 27

Divide 9072000 by 27:

9072000 / 27 = 336000

Now the expression becomes:

336000 * cube root of 3

So, the left side of the equation simplifies to 336000 * cube root of 3.

Now let's simplify the right side of the equation, which is 28√2.

Both sides of the equation are now simplified as:

Left side: 336000 * cube root of 3
Right side: 28√2

To prove that they are equal, we need to show that they have the same value.

Now, it is clear that the left side and right side are not equal. Therefore, there seems to be an error in the given expression or simplification process. Please double-check the original equation or let me know if you need further clarification.