If d=1/2x5 is expressed as a terminating

Jonathan , Magoosh Tutor

Jihan,
I think you're asking why
(2^3 * 5^7) * 2^4 = 2^7 * 5*7 ?

This is multiplication, so we're not "distributing."

(2^3 * 5^7) * 2^4 =

2^3 * 2^4 * 5^7 <-- we can multiply these in any order.

When the bases are the SAME, we add the exponents. If we have the SAME EXPONENT but different bases, we multiply the bases and keep the exponent the same.

2^3 * 2^4 <-- same bases, different exponent =

2^7

2^7 * 5^7 <-- same exponent, different base =

10^7

Apr 14, 2015 • Reply

Hi Mazgab! Great question! You are close here but the two are different.

2^7 * 5^7 is equal to

(2 * 5) ^7

10^7

When you have the same exponent and different bases that are multiplied, you multiply the bases and leave the exponent alone.

The mistake is to think that you add the exponents together. :D

Feb 6, 2015 • Reply