+0

# simplify this expression?

0
374
2

(the answer has to be in positive exponents)

Jul 21, 2017

#2
+20848
+2

simplify this expression?

$$\dfrac{2^{-1}a^2b^{-3}}{4a^3b^{-5}}$$

$$\begin{array}{|rcll|} \hline && \dfrac{2^{-1}a^2b^{-3}}{4a^3b^{-5}} \\\\ &=& \dfrac{2^{-1}a^2b^{-3}}{2^2a^3b^{-5}} \\\\ &=& \dfrac{2^{-1}}{2^2}\cdot \dfrac{a^2}{a^3} \cdot \dfrac{b^{-3}}{b^{-5}} \\\\ &=& \dfrac{1}{2^22^{1}}\cdot \dfrac{1}{a^3a^{-2}} \cdot \dfrac{b^{-3}b^{5}}{1} \\\\ &=& \dfrac{1}{2^{2+1}}\cdot \dfrac{1}{a^{3-2}} \cdot \dfrac{b^{-3+5}}{1} \\\\ &=& \dfrac{1}{2^{3}}\cdot \dfrac{1}{a^{1}} \cdot \dfrac{b^{2}}{1} \\\\ &=& \dfrac{1}{2^{3}}\cdot \dfrac{1}{a} \cdot \dfrac{b^{2}}{1} \\\\ &=& \dfrac{b^{2}}{2^{3}a} \\\\ &=& \dfrac{b^{2}}{8a} \\ \hline \end{array}$$

Jul 21, 2017

#1
0

(b2) / (8a)

Jul 21, 2017
#2
+20848
+2

simplify this expression?

$$\dfrac{2^{-1}a^2b^{-3}}{4a^3b^{-5}}$$

$$\begin{array}{|rcll|} \hline && \dfrac{2^{-1}a^2b^{-3}}{4a^3b^{-5}} \\\\ &=& \dfrac{2^{-1}a^2b^{-3}}{2^2a^3b^{-5}} \\\\ &=& \dfrac{2^{-1}}{2^2}\cdot \dfrac{a^2}{a^3} \cdot \dfrac{b^{-3}}{b^{-5}} \\\\ &=& \dfrac{1}{2^22^{1}}\cdot \dfrac{1}{a^3a^{-2}} \cdot \dfrac{b^{-3}b^{5}}{1} \\\\ &=& \dfrac{1}{2^{2+1}}\cdot \dfrac{1}{a^{3-2}} \cdot \dfrac{b^{-3+5}}{1} \\\\ &=& \dfrac{1}{2^{3}}\cdot \dfrac{1}{a^{1}} \cdot \dfrac{b^{2}}{1} \\\\ &=& \dfrac{1}{2^{3}}\cdot \dfrac{1}{a} \cdot \dfrac{b^{2}}{1} \\\\ &=& \dfrac{b^{2}}{2^{3}a} \\\\ &=& \dfrac{b^{2}}{8a} \\ \hline \end{array}$$

heureka Jul 21, 2017