Algebra Problem:

Question

Simplify: a^p/5b^2ma^4/pb^m/4

(A) a^4p/5b^m/2

(B) a^{(4p^2)/(5)}b^{(m^2/2)}

(C) a^4p/5b^2m/4

(D) a^21p/5b^9m/4

(E) None of the above

For this I got; (D) a^21p/5b^9m/4. Is this correct?

Answer 1

No. When multiplying numbers that have exponents, if the base is the same, we add the exponents. Example: 2² • 2³ = 2⁵

In this case, since a^p/5 is being multiplied by a^4/p, we add the exponents p/5 + 4/p but we need a common denominator to add fractions. That would be 5p. So, multiplying p/5 by p/p we get p²/5p and multiplying 4/p by 5/5 we get 20/5p. Now p²/5p + 20/5p = (p² + 20)/5p so the term becomes a^{(p^2 + 20)/5p}

Since b^2m is being multiplied by b^m/4, the same thing holds, we add 2m and m/4 by getting a common denominator of 4. 2m time 4/4 = 8m/4 and adding m/4 we get b^9m/4 - you got that part correct