# algebra/exponent manipulation help

• February 25th 2010, 04:30 PM
algebra/exponent manipulation help
How do you make 8(.5^(n-1)) turn into 2^(4-n)?
Also what would -8(.5^(n-1)) turn into?

My guess for the first one is to multiply the equation by 2 to get 16x1^(n-1), therefore 16 would be 2^4. Then I get stuck

While the second one, it would be -2^(4-n)? Please explain to me, thank you.
• February 25th 2010, 04:31 PM
Prove It
Quote:

How do you make 8(.5^(n-1)) turn into 2^(4-n)?
Also what would -8(.5^(n-1)) turn into?

My guess for the first one is to multiply the equation by 2 to get 16x1^(n-1), therefore 16 would be 2^4. Then I get stuck

While the second one, it would be -2^(4-n)? Please explain to me, thank you.

$8\left(\frac{1}{2}\right)^{n - 1} = 2^3\cdot 2^{-(n - 1)}$

$= 2^3\cdot 2^{1 - n}$

$= 2^{3 + 1 - n}$

$= 2^{4 - n}$.