Factor and simplify the algebraic expression
3x^-5/4+6x^1/4
My answer is- 3(2x^1/4+1/x^5/4)
nope pull out an x^1/4 and a 3
3x^1/4 (x^-5 +2)
I get
3 x^1/4 (x^-3/2 + 2)
To factor and simplify the algebraic expression, follow these steps:
Step 1: Write the expression in a more simplified form, if possible.
3x^-5/4 + 6x^1/4
Step 2: Simplify the exponents by using the laws of exponents.
x^-5/4 can be rewritten as 1/x^5/4, and x^1/4 remains as it is.
So, the expression can be written as:
3(1/x^5/4) + 6x^1/4
Step 3: Combine the terms with the same base.
The terms do not have the same base, so we cannot combine them directly.
Step 4: Rationalize the denominator.
Since we have a fraction in the exponent, we need to rationalize the denominator.
To rationalize the denominator, multiply the numerator and denominator by x^(4/4) (the conjugate of x^(-5/4)):
((3(1/x^5/4) * x^(4/4)) + (6x^1/4 * x^(4/4))) / (x^(4/4))
Simplifying this gives:
(3x^(4/4 - 5/4) + 6x^(1/4 + 4/4)) / (x^(4/4))
(3x^(-1/4) + 6x^(5/4)) / (x^(1))
Step 5: Simplify further if possible.
Since the terms do not have the same exponent, we cannot combine them further.
So, the simplified form of the algebraic expression is:
(3x^(-1/4) + 6x^(5/4)) / x