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Exponents and fractions

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Source: — Problem Solving |

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by Brent@GMATPrepNow » Thu May 01, 2014 6:42 am
gouldimal wrote:
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
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by unknown13 » Thu May 01, 2014 7:17 pm
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)
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by Brent@GMATPrepNow » Thu May 01, 2014 8:14 pm
It really comes down to what the original question was.
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by gouldimal » Sun May 04, 2014 1:56 pm
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!
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by Brent@GMATPrepNow » Sun May 04, 2014 2:12 pm
gouldimal wrote: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
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