3x^4/5y^2 ÷ 6y^-3/5x^-8
To simplify this expression, we can use the laws of exponents:
First, let's simplify the numerator:
3x^4/5
= 3 * (x^4)^(1/5) (using the property (a^m)^n = a^(m*n))
= 3 * x^(4/5)
Now, let's simplify the denominator:
6y^-3/5x^-8
= 6 * (y^-3/5) * (x^-8)
= 6 * (y^(-3/5)) * (x^(-8))
= 6 / (y^(3/5)) * (1/x^8) (using the property a^(-n) = 1/a^n)
Now, let's divide the numerator by the denominator:
(3 * x^(4/5)) / (6 / (y^(3/5)) * (1/x^8))
= (3 * x^(4/5)) * (y^(3/5)) * (x^8) / 6 (using the rule (a/b) / (c/d) = (a/b) * (d/c))
= (3/6) * x^(4/5 + 8) * y^(3/5)
= (1/2) * x^(4/5 + 40/5) * y^(3/5)
= (1/2) * x^(44/5) * y^(3/5)
Therefore, the simplified expression is (1/2) * x^(44/5) * y^(3/5).
To simplify the expression 3x^4/5y^2 ÷ 6y^-3/5x^-8, we can follow these steps:
Step 1: Simplify both the numerator and denominator separately.
In the numerator, we have 3x^4/5y^2.
In the denominator, we have 6y^-3/5x^-8.
Step 2: Simplify the numerator.
Since there are no like terms to combine in the numerator, it remains as is: 3x^4/5y^2.
Step 3: Simplify the denominator.
First, let's simplify the expression y^-3/5.
Using the property a^(-n) = 1/a^n, we can rewrite y^-3/5 as 1/y^3/5.
Now, let's simplify the expression x^-8.
Using the property a^(-n) = 1/a^n, we can rewrite x^-8 as 1/x^8.
So, the denominator becomes 6(1/y^3/5)(1/x^8).
Step 4: Combine the numerator and denominator.
To divide two fractions, we invert the second fraction and multiply.
So the expression becomes 3x^4/5y^2 * (6x^8)/(y^3/5).
Step 5: Multiply the numerators together and the denominators together.
Multiplying the numerators gives 3 * 6 * x^4 * x^8 = 18x^12.
Multiplying the denominators gives 5 * y^2 * y^3/5 = 5 * y^(2 + 3/5) = 5 * y^(10/5 + 3/5) = 5 * y^13/5.
Step 6: Simplify the expression.
The simplified expression is (18x^12)/(5y^13/5).
To simplify the expression (3x^4/5y^2) ÷ (6y^-3/5x^-8), we can follow these steps:
Step 1: Start by dividing the numerator by the denominator separately.
First, simplify the numerator:
3x^4/5y^2 = (3/5) * x^4 * y^-2
And simplify the denominator:
6y^-3/5x^-8 = (6/5) * y^-3 * x^-8
Step 2: Next, divide each term in the numerator by the corresponding term in the denominator. Remember that dividing by a negative exponent is equivalent to multiplying by the positive exponent.
Divide the coefficients:
(3/5) ÷ (6/5) = (3/5) * (5/6) = 1/2
Divide the x-terms:
x^4 ÷ x^-8 = x^(4 - (-8)) = x^(4 + 8) = x^12
Divide the y-terms:
y^-2 ÷ y^-3 = y^(-2 - (-3)) = y^(-2 + 3) = y^1 = y
Step 3: Combine the results from Step 2 to get the final simplified expression:
(1/2) * x^12 * y
Therefore, the simplified expression is (1/2) * x^12 * y.