SOLUTION: Simplify the radical expression. Assume that all variables are nonnegative real numbers: \root(4)(243x^(8)y^(13)z^(15))

Question 1109001: Simplify the radical expression. Assume that all variables are nonnegative real numbers: \root(4)(243x^(8)y^(13)z^(15))
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
start with:

fourth root of (243 * x^8 * y^13 * z^15)

243 is equivalent to 81 * 3 which is equivalent to (3^4) * 3.
x^8 is equivalent to (x^2)^4.
y^13 is equivalent to (y^3)^4 * y.
z^15 is equivalent to (z^3) * z^3.

your expression is therefore equivalent to:

fourth root of (3^4 * 3 * (x^2)^4 * (y^3)^4 * y * (z^3)^4 * z^3)

everything raised to the fourth power can be removed from under the fourth root sign.

fourth root of (3^4) becomes 3.
fourth root of ((x^2)^4) becomes x^2.
fourth root of ((y^3)^4) becomes y^3.
fourth root of ((z^3)^4) becomes z^3.

your expression becomes:

3 * x^2 * y^3 * z^3 * fourth root of (3 * y * z^3)

i believe it has been simplified as far as it can go.

test the original expression and the final expression with random values of x and y and z.

i did with x = 2, y = 3 and z = 4.

i got 101585.2386 with both the original expression and the final expression.

this confirmed that the conversion was done correctly.

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