factor x^2/7 out of the expression x^5/7-x^2/7
well,
x^5 = x^2 * x^3
so that should get you started...
what confuses you here ?
suppose we just had x^5 - x^2
wouldn't that just be :
x^2( x^3 - 1) ???
so now you have x^(5/7) - x^(2/7)
= x^(2/7) (x^(3/7) - 1)
To factor out x^2/7 from the expression x^5/7 - x^2/7, follow these steps:
Step 1: Identify the common factor.
In this case, the common factor is x^2/7.
Step 2: Rewrite the expression.
Rewrite the expression using the common factor x^2/7 as a factor:
x^5/7 - x^2/7 = (x^5/7) - (x^2/7)
Step 3: Factor out the common factor.
By factoring out x^2/7, we divide each term by x^2/7:
(x^5/7) - (x^2/7) = (x^5/7)/(x^2/7) - (x^2/7)/(x^2/7)
Step 4: Simplify the expression.
To simplify, remember that dividing by a fraction is equivalent to multiplying by its reciprocal:
(x^5/7)/(x^2/7) - (x^2/7)/(x^2/7) = (x^5/7) * (7/x^2) - (x^2/7) * (7/x^2)
Step 5: Combine like terms.
Now, simplify the expression by canceling out like terms:
(x^5/7) * (7/x^2) - (x^2/7) * (7/x^2) = (x^5 * 7) / (7 * x^2) - (x^2 * 7) / (7 * x^2)
Step 6: Finalize the simplified expression.
Simplifying further, we get:
(x^5 * 7) / (7 * x^2) - (x^2 * 7) / (7 * x^2) = x^3 - x^2
Therefore, the factored expression is x^3 - x^2.