Question

Can you please solve these two questions.
Correct answer will be marked as brainliest ​

Answer 1

Answer:

Step-by-step explanation:

ANSWER:

$\frac{\sqrt[4]{625^{-3} }*\sqrt[5]{0.00001}*\sqrt[3]{729}*\sqrt[3]{0.008^{-2}}}{\sqrt[5]{243}*\sqrt[3]{125^{-3}} }$

Solving the numerator first,

$(625)^\frac{-3}{4} \implies 5^{\frac{-3*4}{4} } \implies 5^{-3}$

$(\frac{1}{10000} )^{\frac{1}{5}} \implies (\frac{1}{10} )^{\frac{5}{5}} \implies \frac{1}{10}$

$\sqrt[3]{729} \implies 9$

$\sqrt[3]{0.008^{-2}} \implies (\frac{8}{1000} )^{\frac{-2}{3}} \implies (\frac{2}{10} )^{\frac{-2*3}{3}} \implies (0.2)^{-2}$

$5^{-3+(-2)}+\frac{1}{10} \implies 5^{-5}*\frac{1}{10}$

Now Denominator :-

$\sqrt[5]{243} \implies 3$

$\sqrt[3]{125^{-3}} \implies (5)^\frac{-3}{3} \implies 5^{-1}$

$3*5^{-1}$

Putting Numerator and Denominator in Order,

$\frac{5^{-3}*5^3*9}{3*(0.2)^2*10}$

$\frac{5^{-3}*5^3*9}{3*0.04*10}$

$\frac{100*3}{10*4}$ where one zero of 100 and 10 cancels,

$\frac{30}{4}$ is the required answer.

1st Answer:

First we will add 1 and minus 1 to all the Equation so that the equation remains the same.

$\frac{1}{x+1}(-1+1) + \frac{2}{y+2} (-1+1) +\frac{2006}{z+2006} (-1+1)=1$

Taking LCM with -1,

$\frac{1-x-1}{x+1} +1+\frac{2-y-2}{y+2}+1+\frac{2006-2-2006}{z+2006}+1=1$

positive and negative in numerator of each fraction cancels off, +3 goes to other side and becomes +1-3 = -2.

$\frac{-x}{x+1} +\frac{-y}{y+z} + \frac{-z}{z+2006} = -2$

Taking Negative common and it cancels, The required answer is 2.

Answer 2

$[tex] \frac{ \sqrt[4]{(625)^{ - 3} } \times \sqrt[5]{0.00001} \times \sqrt[3]{729} \times \sqrt[3]{(0.008)^{ - 2} } }{ \sqrt[5]{243} \times \sqrt[3]{ {(125)}^{ - 3} } } \\ \\ = \frac{ {5}^{ - 3} \times 0.1 \times 9 \times {(0.2)}^{ - 2} }{3 \times {(5)}^{ - 3} } \\ \\ = \frac{ {5}^{ - 3} \times {5}^{3} \times 1 \times 9 }{3 \times {(0.2)}^{2} \times 10 } \\ \\ = \frac{ \cancel{{5}^{ - 3}} \times \cancel{{5}^{3}} \times 1 \times \cancel{9}}{\cancel{3} \times 0.04\times 10 } \\ \\ = \frac{ 10 \times \cancel{10} \times 3}{4 \times \cancel{10}} \\ \\ = \frac{30}{4}$[/tex]

Answer is 30/4 .