Number Properties - Exponent Rules

[Absco]

Hi all,

I'm having trouble getting my head around this question:

What is the value of m?

1.)
4^m + 4^m + 4^m + 4^m
______________________ = 1
2^(m+2) - 2^(m+1)


2.)
m^3 × m^4
_________ = 1
m^5

I can see that 2.) is m^7/m^5 = m^2. The value for m is therefore +/- 1, therefore insufficient.

But I'm not sure if my calculations are the best way to work out how 1.) is sufficient. This is how I've done it:

4^(m+1)
_______ = 1
2^(m+1)

then maybe:

2^(m+1) x 2^(m+1)
_________________ = 1
2^(m+1)

and then:

2^(m+1) = 1

which means m = -1?

[Brent@GMATPrepNow]

Hi all,

I'm having trouble getting my head around this question:

What is the value of m?

1.)
4^m + 4^m + 4^m + 4^m
______________________ = 1
2^(m+2) - 2^(m+1)


2.)
m^3 × m^4
_________ = 1
m^5

I can see that 2.) is m^7/m^5 = m^2. The value for m is therefore +/- 1, therefore insufficient.

But I'm not sure if my calculations are the best way to work out how 1.) is sufficient. This is how I've done it:

4^(m+1)
_______ = 1
2^(m+1)

then maybe:

2^(m+1) x 2^(m+1)
_________________ = 1
2^(m+1)

and then:

2^(m+1) = 1

which means m = -1?

Your calculations are perfect.

For those who don't see the leap you made for statement 1, here are the steps

4^m + 4^m + 4^m + 4^m
______________________ = 1
2^(m+2) - 2^(m+1)

4(4^m)
_______________ = 1
(2^m+1)(2^1 - 1)

4^(m+1)
___________ = 1
2^m+1(1)

4^(m+1)
_______________ = 1
2^(m+1)


2^(m+1)= 1 (this last step uses the rule (a^x)/(b^x) = (a/b)^x

If 2^(m+1)= 1, then m+1 = 0, which means m=-1

Cheers,
Brent