Question

Quick help with this problem, help!

Answer 1

5/4

Explanation:

You want the product abc when 5x^-2y^(3/2)/√(25xy^4) is written as ax^by^c.

Rules of exponents

The applicable rules of exponents are ...

`a^ba^c=a^(b+c)\\\\(1)/(√(a))=a^{-(1)/(2)}\\\\(a^b)^c=a^(bc)`

Application

Using these rules, the expression can be simplified to ...

`\frac{5x^(-2)y^{(3)/(2)}}{√(25xy^4)}=(5x^(-2)y^{(3)/(2)})(5^2xy^4)^{-(1)/(2)}=(5x^(-2)y^{(3)/(2)})(5^{2(-(1)/(2))}x^{-(1)/(2)}y^{4(-(1)/(2))})\\\\=5^(1-1)x^{-2-(1)/(2)}y^{(3)/(2)-2}\\\\=1\cdot x^{-(5)/(2)}y^{-(1)/(2)}`

From this last expression, we determine ...

• a = 1
• b = -5/2
• c = -1/2

Product

The product of the values of interest is ...

abc = (1)(-5/2)(-1/2)

abc = 5/4