If 34x-81-1-and-101-y-0-0001-find-the-value-of-2-x-4y-

3^4x=(81)^ 1,10^1/y=0.0001 3^4x=(3^4)^ 1⇒ 3^4x=(3)^ 4 ∴ 4x= 4⇒ x= 4/4= 1,and 10^1/y=0.0001=1/10000=1/(10)^4=(10)^ 4 ∴1/y= 4⇒ y= 1/4 Now,2^ x+4y=2^ ( 1)+4 ( 1/4 ...

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Standard IX

Mathematics

Laws of Exponents for Real Numbers

If 34x=81-1 a...

Question

If $3^{4 x} = (81)^{- 1} a n d 10^{\frac{1}{y}} = 0.0001, f i n d t h e v a l u e o f 2^{- x + 4 y} .$

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Solution

$3^{4 x} = (81)^{- 1}, 10^{\frac{1}{y}} = 0.0001 3^{4 x} = (3^{4})^{- 1} \Rightarrow 3^{4 x} = (3)^{- 4} ∴ 4 x = - 4 \Rightarrow x = \frac{- 4}{4} = - 1, a n d 10^{\frac{1}{y}} = 0.0001 = \frac{1}{10000} = \frac{1}{(10)^{4}} = (10)^{- 4} ∴ \frac{1}{y} = - 4 \Rightarrow y = - \frac{1}{4} N o w, 2^{- x + 4 y} = 2^{- (- 1) + 4 (\frac{- 1}{4})} = 2^{1 - 1} = 2^{0} = 1$

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If 34x=(81)−1 and 101y=0.0001,find the value of 2−x+4y.

34x=(81)−1,101y=0.000134x=(34)−1⇒34x=(3)−4∴4x=−4⇒x=−44=−1,and101y=0.0001=110000=1(10)4=(10)−4∴1y=−4⇒y=−14Now,2−x+4y=2−(−1)+4(−14)=21−1=20=1

If $3^{4 x} = (81)^{- 1} a n d 10^{\frac{1}{y}} = 0.0001, f i n d t h e v a l u e o f 2^{- x + 4 y} .$