5y^3(y^5)2
_______________
10y^5(y^2)^6
5y^3 * y^10
_______________
10y^5* y^12
5y^30
_______________
10y^19
To simplify the expression (5y^3(y^5)2) ÷ (10y^5(y^2)^6), we can follow these steps:
Step 1: Apply the power of a power rule:
In this step, we multiply the exponents of the same base.
The numerator: 5y^3(y^5)2 = 5y^3 * y^10 = 5y^13
The denominator: 10y^5(y^2)^6 = 10y^5 * y^12 = 10y^17
Step 2: Simplify the expression further:
Now we can divide the numerator by the denominator.
The expression becomes:
(5y^13) / (10y^17)
Again, we can further simplify this expression by dividing both the numerator and denominator by the greatest common factor:
The greatest common factor of 5 and 10 is 5.
The greatest common factor of y^13 and y^17 is y^13.
Therefore, we have:
(5y^13) / (10y^17) = (y^13) / (2y^4)
And that is the simplified expression.