Square root of X exponent 4 y over
4 Square root of X exponent 2 y exponent 8
equals X exponent 2 over Y exponent 7
equals X -2X-1/3 (WHY?)
equals X3/2 square root of y/y exponent 2 (WHY?)
*I understand this is the answer, but when I look at what my teacher wrote, I do not understand the steps. Please help me with the steps!
√(x^4y) / 4√(x^2y^8)
Now, you know that √x^2 = x, so you have
(x^2 √y) / 4xy^4
= x√y / 4y^3
Apparently I have not parsed you English words correctly into algebra. Using my symbols (copy/paste), repost so the algebra is clear.
At any rate, just recall that
√x = x^(1/2)
√(x^n) = x^(n/2)
(x^a)^b = x^(ab)
x^a/x^b = x^(a-b)
To understand the steps for simplifying the given expression, let's break it down step by step:
Step 1: Simplify the numerator.
The numerator is the expression -4√(X^4y). We can simplify this by breaking down the square root.
√(X^4y) = √(X^4) * √y = X^2 * √y
So, the numerator simplifies to -4X^2√y.
Step 2: Simplify the denominator.
The denominator is the expression 4√(X^2y^8). Similarly, we break down the square root.
√(X^2y^8) = √(X^2) * √(y^8) = X * y^4
So, the denominator simplifies to 4Xy^4.
Step 3: Simplify the entire expression.
Now, substitute the simplified numerator and denominator back into the original expression:
(-4X^2√y) / (4Xy^4)
Step 4: Cancel out common factors.
In the numerator and denominator, we can cancel out the common factors. In this case, both the numerator and denominator have a 4, an X, and a y^4, so they can be canceled out.
(-4X^2√y) / (4Xy^4) = (-1X^2√y) / (y^4)
Step 5: Simplify the exponent.
Rewriting the expression (-1X^2√y) / (y^4) as a fraction, we can simplify the exponents.
(-1X^2√y) / (y^4) = (-1X^2√y) / (y^2 * y^2) = -X^2√y / (y^2)^2
Step 6: Simplify the square root and exponent.
The expression -X^2√y / (y^2)^2 can be written as:
-X^2√y / y^4 = -X^2(y/y^2)^(1/2) / y^4 = -X^2(y/y^2)^(1/2-y^4) = -X^2(y/y^2)^(1/2-2) = X^2(y^(-1/2)) = X^2/y^(1/2)
Step 7: Simplify the radical in the denominator.
The expression X^2/y^(1/2) can be written as:
X^2/y^(1/2) = X^2 * (y^(1/2))^(-1)
= X^2 * (1/y^(1/2))
= X^2 / y^(1/2)
= X^2 / √y
Therefore, the final simplified expression is X^2 / √y.