# simplify by eliminating the zero exponent & negative exponent

• Aug 19th 2008, 01:11 AM
eepyej
simplify by eliminating the zero exponent & negative exponent
& express powers with fractional exponent in their radical forms

1. (3^x+2)(a^2)(b^4x-1)(c^3) / (3^2)(a^3/2)(b^2x)(c^x+1/2)
• Aug 19th 2008, 09:41 AM
Soroban
Hello, eepye!

The problem is not clear . . . You need more parentheses.
I will guess at what you meant.

Quote:

Express powers with fractional exponent in their radical forms

$1.\;\;\frac{3^{x+2}\cdot a^2\cdot b^{4x-1}\cdot c^3} {3^2\cdot a^{\frac{3}{2}}\cdot b^{2x}\cdot c^{\frac{x+1}{2}}}$

We have: . $\frac{3^{x+2}}{3^2} \cdot \frac{a^2}{a^{\frac{3}{2}}} \cdot \frac{b^{4x-1}}{b^{2x}} \cdot \frac{c^3}{c^{\frac{x+1}{2}}}$

. . . . . . $= \;\;3^{(x+2)-2} \cdot a^{2-\frac{3}{2}} \cdot b^{(4x-1) - 2x} \cdot c^{3 - \frac{x+1}{2}}$

. . . . . . $=\;\;3^x\cdot a^{\frac{1}{2}}\cdot b^{2x-1}\cdot c^{\frac{5-x}{2}}$

. . . . . . $= \;\;3^x\cdot\sqrt{a}\cdot b^{2x-1} \cdot\sqrt{c^{5-x}}$

. . . . . . $=\;\;3^x b^{2x-1}\sqrt{ac^{5-x}}$