I need help simplifying this expression:
(3x^3y^5 + 6x^2y^-2/6x^5y^-2)^2
(3x^3y^5 + 6x^2y^-2/6x^5y^-2)^2
the second term has a y^-2 in the numerator and denominator, so..
(3x^3y^5 + 6x^2 /6x^5 )^2
(3x^3y^5 + 1 /x^3 )^2
I am not certain much more can be done to simplify it.
To simplify the given expression, we can follow these steps:
Step 1: Address the exponent in the denominator.
Since we have y^(-2) in the denominator, we can move it to the numerator by changing its sign. This gives us:
(3x^3y^5 + 6x^2 / 6x^5y^(2))^2
Step 2: Simplify the fraction.
To combine the terms in the numerator, we add the exponents when the bases are the same. So we can rewrite the expression as:
(3x^3y^5 + 6x^2 / 6x^5y^2)^2
Step 3: Simplify within the parentheses.
Now let's simplify the fraction within the parentheses by dividing each term by 6x^5y^2. This yields:
(1/2x^2y^3 + 1/x^3)^2
Step 4: Simplify by squaring the expression.
Next, we square each term within the parentheses using the rule (a + b)^2 = a^2 + 2ab + b^2. Applying this rule yields:
(1/2x^2y^3)^2 + 2(1/2x^2y^3)(1/x^3) + (1/x^3)^2
Simplifying this expression further gives us:
1/4x^4y^6 + 2(1/2x^5y^3) + 1/x^6
Step 5: Combine like terms.
Finally, combine the like terms in the expression, which gives us the simplified form:
1/4x^4y^6 + 1/x^4y^3 + 1/x^6