$(\frac{a^{2} b^{- 3} c^{- 5}}{a^{5} b^{- 7} c^{- 8}}) \cdot (\frac{\sqrt{a^{3} b^{- 9}}}{\sqrt[3]{c^{8}}}) = \sqrt[6]{\frac{c^{2}}{a^{9} b^{3}}}$
True
False

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The given equation is $False$

Steps

Step 1 ：Simplify the left side of the equation: $(\frac{a^{2} b^{- 3} c^{- 5}}{a^{5} b^{- 7} c^{- 8}}) \cdot (\frac{\sqrt{a^{3} b^{- 9}}}{\sqrt[3]{c^{8}}}) = b^{4} c^{3} \sqrt{\frac{a^{3}}{b^{9}}} \div a^{3} \sqrt[3]{c^{8}}$

Step 2 ：Simplify the right side of the equation: $\sqrt[6]{\frac{c^{2}}{a^{9} b^{3}}} = \sqrt{\frac{c^{2}}{a^{9} b^{3}}}$

Step 3 ：Compare the simplified left and right sides of the equation: $b^{4} c^{3} \sqrt{\frac{a^{3}}{b^{9}}} \div a^{3} \sqrt[3]{c^{8}}$ is not equal to $\sqrt{\frac{c^{2}}{a^{9} b^{3}}}$

Step 4 ：Final Answer: The given equation is $False$

(a2b−3c−5a5b−7c−8)⋅(a3b−9c83)=c2a9b36TrueFalse

Answer

Popular Problems

$(\frac{a^{2} b^{- 3} c^{- 5}}{a^{5} b^{- 7} c^{- 8}}) \cdot (\frac{\sqrt{a^{3} b^{- 9}}}{\sqrt[3]{c^{8}}}) = \sqrt[6]{\frac{c^{2}}{a^{9} b^{3}}}$
True
False