Simplifying the Expression: 2x^3y^5/5(x^4y^2)^3
In this article, we will simplify the algebraic expression 2x^3y^5/5(x^4y^2)^3 using the rules of indices and the properties of fractions.
Step 1: Simplify the Denominator
The denominator of the expression is 5(x^4y^2)^3. To simplify this, we need to apply the power rule of indices, which states that (x^n)^m = x^(n*m).
(x^4y^2)^3 = x^(43)y^(23) = x^12y^6
So, the denominator becomes 5x^12y^6.
Step 2: Simplify the Numerator
The numerator of the expression is 2x^3y^5. There is no simplification needed for the numerator.
Step 3: Simplify the Entire Expression
Now, we can simplify the entire expression by dividing the numerator by the denominator.
2x^3y^5 / 5x^12y^6
To divide the numerator by the denominator, we need to subtract the exponents of the denominator from the exponents of the numerator.
x^(3-12)y^(5-6) = x^(-9)y^(-1)
Since x^(-n) = 1/x^n, we can rewrite the expression as:
2/(5x^9y)
Final Answer
The simplified expression is:
2/(5x^9y)
In conclusion, we have successfully simplified the expression 2x^3y^5/5(x^4y^2)^3 to 2/(5x^9y) using the rules of indices and the properties of fractions.
