Is the answer to, 3x^4/5y^2 ÷ 6y^-3/5x^-8, y/2x^4. Show your work.
To simplify the expression 3x^(4/5)y^2 ÷ 6y^(-3/5)x^(-8), we can first simplify the exponents and combine like terms:
3x^(4/5)y^2 ÷ 6y^(-3/5)x^(-8)
= (3/6) * (x^(4/5) / x^(-8)) * (y^2 / y^(-3/5))
Next, we can simplify each term individually:
x^(4/5) / x^(-8) = x^(4/5 - (-8)) = x^(4/5 + 8) = x^(44/5)
y^2 / y^(-3/5) = y^(2 - (-3/5)) = y^(2 + 3/5) = y^(13/5)
Substituting these simplified terms back into the expression:
(3/6) * (x^(44/5)) * (y^(13/5))
Next, we can simplify the fraction 3/6 which is equivalent to 1/2:
(1/2) * (x^(44/5)) * (y^(13/5))
Finally, we can rewrite the exponents in terms of radicals:
(1/2) * ( √(x^44) ) * ( √(y^13) )
Simplifying the expression further would require further information about the values of x and y.
To simplify the expression, 3x^4/5y^2 ÷ 6y^-3/5x^-8, we'll follow these steps:
Step 1: Division with exponents
3x^(4/5)y^2 ÷ (6y^(-3/5)x^(-8))
Step 2: Simplify the coefficients
(3/6)x^(4/5)y^2y^(3/5)x^8
Step 3: Combine variables with the same base by adding their exponents
(1/2)x^(4/5+8)y^(2+(3/5))
Step 4: Simplify the exponents
(1/2)x^(4/5+40/5)y^(10/5+3/5)
Step 5: More exponent simplification
(1/2)x^(44/5)y^(13/5)
Step 6: Rewrite the expression
(1/2)(x^(44/5)y^(13/5))
So, the simplified expression is ((1/2)(x^(44/5)y^(13/5))), which is not equal to y/2x^4.
To simplify the expression 3x^4/5y^2 ÷ 6y^-3/5x^-8, we can follow these steps:
Step 1: Combine the division operation
Dividing two terms is the same as multiplying by the reciprocal of the second term. So, we can rewrite the expression as follows:
3x^4/5y^2 * 5x^-8/6y^-3
Step 2: Simplify the variables
When multiplying terms with the same base, we can add their exponents. Apply this rule to simplify the expression:
(3/5) * (x^4 * x^-8) / (y^2 * y^-3)
Simplifying further:
(3/5) * (x^(4-8)) / (y^(2-3))
(3/5) * (x^-4) / (y^-1)
Step 3: Simplify the exponents
A negative exponent can be transformed into a positive exponent by moving the term to the denominator or vice versa. Rewrite the expression with positive exponents:
(3/5) * (1/x^4) * (y^1)
Step 4: Combine the terms
Multiply the coefficients and combine the remaining terms:
3/5xy^1 * 1/x^4
Simplifying further:
3/5xy
So, the simplified form of the expression 3x^4/5y^2 ÷ 6y^-3/5x^-8 is 3/5xy.