%5E5%2F4.jpeg "(x^-4/y^-10)^5/4")
Simplifying the Expression (x^-4/y^-10)^5/4
In this article, we will simplify the expression (x^-4/y^-10)^5/4 using the laws of exponents.
Step 1: Apply the Power Rule
The power rule states that (a^m)^n = a^(mn). Applying this rule to our expression, we get:
((x^-4/y^-10)^5)^(1/4)
Step 2: Expand the Expression
Expanding the expression, we get:
(x^(-4*5)/y^(-10*5))^(1/4)
Simplifying further, we get:
(x^(-20)/y^(-50))^(1/4)
Step 3: Simplify the Expression
Now, we can simplify the expression by applying the power rule again:
(x^(-20/4))/(y^(-50/4))
(x^-5)/(y^-12.5)
Step 4: Write in Standard Form
Finally, we can write the simplified expression in standard form:
y^(12.5) / x^5
Therefore, the simplified form of the expression (x^-4/y^-10)^5/4 is y^(12.5) / x^5.
Note: The laws of exponents are essential in simplifying expressions involving exponents. In this example, we applied the power rule and the quotient rule to simplify the expression.
