81 has negative powers?

Algebra Level 2

$\Large \left ( \color{#69047E}{81} \right )^{ - \left (\color{#20A900}2^{- \color{#3D99F6}2} \right ) } = \ ?$

\cfrac { 1 }{ 3 }

3

81

{ 81 }^{ 4 }

None of the above

6 solutions

Vaibhav Prasad
Mar 25, 2015

$\huge {({ \left( 81 \right) }^{ -\left( { 2 }^{ -2 } \right) })\\ \Rightarrow ({ \left( 81 \right) }^{ -\left( \frac { 1 }{ { 2 }^{ 2 } } \right) })\\ \Rightarrow ({ \left( 81 \right) }^{ -\left( \frac { 1 }{ 4 } \right) })\\ \Rightarrow \frac { 1 }{ { 81 }^{ \frac { 1 }{ 4 } } } \\ \Rightarrow \boxed {\frac { 1 }{ 3 }} }$

Upvote it if you like it

Soumo Mukherjee
Mar 25, 2015

$\Large { \left( 81 \right) }^{ -\left( { 2 }^{ -2 } \right) }={ \left( 81 \right) }^{ -{ 1 }/{ 4 } }=\cfrac { 1 }{ { \left( { 3 }^{ 4 } \right) }^{ { 1 }/{ 4 } } } =\cfrac { 1 }{ 3 }$

Alright I want to know who is changing names of my problems? I get it, you are trying to clarify it. But I want to know who is changing them . To him I want to tell that, whatever he changes the name to, 'I Do not Like Putting The Answer In The Name.'

Next time whenever you find that I have attached an inappropriate name to a problem please keep that in mind. However, there wasn't any need to modify it.

I don't appreciate such alterations, really I don't.

Calvin Edit: Brilliant updates the popular problems, to make it easier for someone to decide if they want to work on them. This would include editing the title, improving the display in the feeds, and adding an appropriate image.

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Soumo Mukherjee - 6 years, 2 months ago

Updated! Your profile has changed, and it might take a while for the rest of the site's cache to update.

Calvin Lin Staff - 6 years, 2 months ago

Yeah, thanks a lot. 'm really happy now.

This site has the best staff-user interaction.

^_^

Soumo Mukherjee - 6 years, 2 months ago

Lew Sterling Jr
Mar 29, 2015

Upvote my steps if you like this explanation

@Llewellyn Sterling :

$\frac{1}{81^{\left(2^{-2}\right)}} \neq \frac{1}{81^{-4}} \neq \frac{1}{81^{-\frac{1}{4}}} \neq \frac{1}{\sqrt[4]{81}}.$

Instead,

$\frac{1}{81^{\left(2^{-2}\right)}} = \frac{1}{81^{\left(\frac{1}{2^2}\right)}} = \frac{1}{81^{\frac{1}{4}}}=\frac{1}{\sqrt[4]{3^4}}=\boxed{\frac{1}{3}}.$

Please edit your solution. Thanks! :)

Victor Loh - 6 years, 2 months ago

I forgot to add a note next to the wrong step, @Victor Loh . Thanks for noticing.

Lew Sterling Jr - 6 years, 2 months ago

Carl Cristobal
Apr 1, 2015

= {81} ^ -(2 ^ -2)

= {81} ^ -(1/4)

= 1 / { 81 ^ (1/4) }

= 1 / { (3^4) ^ (1/4) }

= 1 / { 3 ^ (4/4) }

= 1/ { 3 }

= 1/3

Diana Ir
Apr 2, 2015

81 is simplified to a smaller number and is the same as saying 3^4. So our equation now looks like this: 3^-4(2^-2). The 2^-2 is the same as saying 1/2^2 which is the same as saying 1/4. So now we have 3^-4/4, which equals 3^-1. The 3^-1 is the same as saying 1/3. The answer is 1/3.

Gabriel Genellina
Apr 1, 2015

Type 81^-(2^-2) on the scratchpad and you're done.

81 has negative powers?

6 solutions

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