15sqrt8x^16/5sqrt2x^4
*you have to simplify,but I don't get this one at ALL!PLease help...
To simplify the expression 15sqrt(8x^16) / 5sqrt(2x^4), we can break down the square roots and simplify the terms separately.
First, let's simplify the numerator: sqrt(8x^16).
Step 1: Simplify the square root of the number 8:
sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2 * sqrt(2) = 2sqrt(2).
Step 2: Simplify the square root of x^16:
sqrt(x^16) = sqrt((x^8)^2) = x^8.
Putting it together, the numerator becomes: 2sqrt(2) * x^8.
Now, let's simplify the denominator: sqrt(2x^4).
Step 3: Simplify the square root of the number 2:
sqrt(2).
Step 4: Simplify the square root of x^4:
sqrt(x^4) = sqrt((x^2)^2) = x^2.
Putting it together, the denominator becomes: sqrt(2) * x^2.
Now, combining the simplified numerator and denominator, we get:
(2sqrt(2) * x^8) / (sqrt(2) * x^2).
To simplify this further, we can cancel out common factors between the numerator and denominator.
Step 5: Simplify the common factor of sqrt(2):
(2sqrt(2) * x^8) / (sqrt(2) * x^2) = (2 * x^8) / x^2.
Step 6: Simplify the x terms:
(2 * x^8) / x^2 = 2x^6.
So the simplified expression is 2x^6.