X^4 Y^.5 Z SQAURE ROOT 3

________________________
Y^-7 Z^0 X^5

CAN SOMEONE HELP BREAK DOWN THIS PROBLEM SO I CAN LEARN TO DO IT STEP BY STEP??

√3 = 3^.5

z^0 = 1

So, we can write this as

x^4 y^.5 z 3^.5
------------------- = (y^6.5 3^.5/x) = √(3y)y^6/x
y^-6 x^5

rats:

√3y y^6 z
--------------
x

Of course! Let's break down this problem step by step.

The expression is:
(X^4 * Y^0.5 * Z * √3) / (Y^-7 * Z^0 * X^5)

Step 1: Simplify the exponents.
- Any number raised to the power of 0 is equal to 1, so we can simplify Y^0 and Z^0 to be 1.
- The square root (√) is the same as raising the number to the power of 0.5, so we can simplify Y^0.5 to √Y.
- Now the expression becomes:
(X^4 * √Y * Z * √3) / (Y^-7 * X^5)

Step 2: Combine like terms.
- Combine the X terms in the numerator and denominator: X^4 / X^5 = X^(4 - 5) = X^(-1).
- The expression becomes:
(√Y * Z * √3) / (Y^-7 * X^-1)

Step 3: Deal with negative exponents.
- A negative exponent can be moved to the denominator by changing its sign: Y^-7 = 1 / Y^7, and X^-1 = 1 / X.
- Now the expression becomes:
(√Y * Z * √3) / (1 / Y^7 * 1 / X)

Step 4: Simplify the expression.
- Multiplying by 1 / Y^7 is the same as dividing by Y^7, and multiplying by 1 / X is the same as dividing by X.
- The expression simplifies to:
(√Y * Z * √3 * Y^7) / X

So, the final simplified expression is:
(√Y * Z * √3 * Y^7) / X

I hope this step-by-step breakdown helps you understand how to approach this problem!