anonymous
  • anonymous
What value of m solves the equation? 2^m = 1/8
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
mathstudent55
  • mathstudent55
Have you learned negative exponents?

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anonymous
  • anonymous
doing it now .-. most annoying thing ever.
mathstudent55
  • mathstudent55
\(\large a^{-n} = \dfrac{1}{a^n} \)
mathstudent55
  • mathstudent55
First, rewrite the fraction 1/8 as 1 over a power of 2. 8 is 2 to what power?
mathstudent55
  • mathstudent55
\(\large 2^? = 8\)
anonymous
  • anonymous
I dont know. ;-;
anonymous
  • anonymous
do you know the answer?
anonymous
  • anonymous
\[2 \times 2 = ?\]
mathstudent55
  • mathstudent55
\(8 = 2 \times 2 \times 2\) Ok?
mathstudent55
  • mathstudent55
How do you write \(2 \times 2 \times 2\) as 2 raised to an exponent?
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
Do you understand now how you write 8 as a power of 2? \(\large 8 = 2 \times 2 \times 2 = 2^3\)
anonymous
  • anonymous
He's offline.
anonymous
  • anonymous
im back sorry XD
anonymous
  • anonymous
im getting way too angry about this i need the answer
mathstudent55
  • mathstudent55
Once you know that \(8 = 2^3\), now you can replace 8 with \(2^3\) in the fraction. \(\large 2^m = \dfrac{1}{2^3} \) Ok so far?
mathstudent55
  • mathstudent55
Now we look again at the definition of a negative exponent. \(\large a^{-n} = \dfrac{1}{a^n}\) We have \(\large \dfrac{1}{2^3} \) Compare the fraction above with the definition of negative exponent.
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
The base of the power in the denominator becomes the base. Then the exponent of the denominator becomes the negative of the exponent.
mathstudent55
  • mathstudent55
|dw:1440520193790:dw|
anonymous
  • anonymous
\[2^{m} = \frac{ 1 }{ 2^{3}}\]
anonymous
  • anonymous
\[a ^{-m} = \frac{ 1 }{ a ^{m} }\]
anonymous
  • anonymous
do you know the answer? .-. dude ive only got about 3 minutes before i have to leave. please help me.
anonymous
  • anonymous
The answer has already been given.
anonymous
  • anonymous
Look at the equations I posted above you.
anonymous
  • anonymous
canI need to know what m is
mathstudent55
  • mathstudent55
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