Exponents. Why am I wrong?

[Kit]

Hello mathy people. I have a little “why am I wrong” puzzle for you.

Find k.

3^3+3^3+3^3=243*3^k

my working

27+27+27=81.   243/3=81      3^-3=1/3

thus 81= 243*3^-3

Their working.

3^3+3^3+3^3=3^1*3^3=3^4      243=3^4*3^1   We need to get rid of the 3^1 thus k=  -1 

As usual I can see why their way works, but not what I have done wrong with mine....

Thank you.....

 

 

[Caroline]

4 minutes ago, Kit said:

Hello mathy people. I have a little “why am I wrong” puzzle for you.

Find k.

3^3+3^3+3^3=243*3^k

my working

27+27+27=81.   243/3=81      3^-3=1/3

thus 81= 243*3^-3

Their working.

3^3+3^3+3^3=3^1*3^3=3^4      243=3^4*3^1   We need to get rid of the 3^1 thus k=  -1 

As usual I can see why their way works, but not what I have done wrong with mine....

Thank you.....

 

 

3^(-3) is 1/27 not  1/3. 3^(-1) is 1/3. 

[Kit]

Just now, Caroline said:

3^(-3) is 1/27 not  1/3. 3^(-1) is 1/3. 

Seriously! An arithmetic mistake! Opps! Thank you so much.

while you are here, you couldn’t please give me a hint on where to start with 

Express 2^12 as a power of 1/8 

Not the answer, just an angle of attack please.

Thank you.

 

 

[Caroline]

2 minutes ago, Kit said:

Seriously! An arithmetic mistake! Opps! Thank you so much.

while you are here, you couldn’t please give me a hint on where to start with 

Express 2^12 as a power of 1/8 

Not the answer, just an angle of attack please.

Thank you.

 

 

Think of how to express 1/8 as a power of 2. 2^what=1/8

[Kit]

1 minute ago, Caroline said:

Think of how to express 1/8 as a power of 2. 2^what=1/8

Thank you. I’m off to the sofa with my notebook and a cuppa to consider this.

[Kit]

I got it! Thank you for the tip off.

i wallowed a bit 2^n =1/8     2*2*2=8 gotta go fractions....so negative? 2^-3?Tested it     2^-3 =1/2^3 =1/8

The I realised, after a bit,  looking at the above, what we actually needed was 2^12=8^n and then simply negate the answer.

so this is my working

2^12 = 2^n*2^n*2^n (negated)

= 2^n+n+n (what 3 numbers added make 12?)

Thus 2^12=2^4*2^4*2^4 =8^4(negated) 

And 8^4 negated is 1/8^-4. One eighth to the power of negative 4

phew! 
 

Thank you for the tip off, I appreciate it.