Exponents and fractions

[gouldimal]

First post, so please bear with me. I am struggling with the first steps on this problem:

5^3 x (5^4)^y / (5^y)^3

[Brent@GMATPrepNow]

5^3 x (5^4)^y / (5^y)^3

I'm assuming that the "x" is a variable and not a multiplication symbol.
I'm also assuming that 5^3 x = (5^3)(x)

We have (5^3)(x) (5^4)^y / (5^y)^3

Let's deal with (5^4)^y / (5^y)^3 first.
(5^4)^y = 5^4y [power of a power rule]
(5^y)^3 = 5^3y [power of a power rule]
So, (5^4)^y / (5^y)^3 = (5^4y)/(5^3y) = 5^y [quotient rule]


So, we have (5^3)(x) (5^y) = (x)(5^3) 5^y
= (x)[5^(3 + y)]

Of course, this won't be correct unless I'm right about my assumptions regarding the original question

Cheers,
Brent

[unknown13]

Hi
I solved using the simple principles of powers
(5^4)^y = 5^4y
(5^y)^3 = 5^3y
now
(5^4y) / (5^3y) = 5^(4y-3y) = 5^y
as per the principle of multiplication
5^3 * 5^y = 5^(3+y)

[Brent@GMATPrepNow]

It really comes down to what the original question was.

[gouldimal]

Brent, I think I may have confused things with the x, as it was meant to be multiplication, not a second variable. Is there a better convention for writing problems?

Thanks!

[Brent@GMATPrepNow]

Brent, I think I may have confused things with the x, as it was meant to be multiplication, not a second variable. Is there a better convention for writing problems?

Thanks!

For multiplication, it's best to just place the parts in brackets. For example, write (5)(3) rather than 5 x 3

So, we have (5^3) (5^4)^y/(5^y)^3

Let's deal with (5^4)^y / (5^y)^3 first.
(5^4)^y = 5^4y [power of a power rule]
(5^y)^3 = 5^3y [power of a power rule]
So, (5^4)^y / (5^y)^3 = (5^4y)/(5^3y) = 5^y [quotient rule]

This gives us (5^3) (5^y) = 5^(3 + y)

Cheers,
Brent