Question

Factor, using the common factor, 4a^17. Assume all variables represent positive real numbers. -4a^-5/4+8a^-17/14 =

(Simplify your answer.)​

Answer 1

To factor the expression -4a^(-5/4) + 8a^(-17/14), you can first factor out the common factor of 4a^(-17/14), which is the lowest exponent between the two terms:

-4a^(-5/4) + 8a^(-17/14) = 4a^(-17/14) * (-a^(1 + 3/4) + 2)

Now, let's simplify the expression inside the parentheses:

-a^(1 + 3/4) + 2 = -a^(4/4 + 3/4) + 2 = -a^(7/4) + 2

Now, you have:

4a^(-17/14) * (-a^(7/4) + 2)

This is the factored form of the expression.