(6^14*5^13) - (6^13*5^14) =

Question

(6^{14}*5^{13})-(6^{13}*5^{14})= A. 0 B. 1 C. 30 D. 11^{13} E. 30^{13} 2024-01-26_13-57-54.png

Bunuel · Accepted Answer

(6^{14}*5^{13})-(6^{13}*5^{14})=

A.  0

B.  1

C.  30

D.  11^{13}

E.  30^{13} 
____________________________________
 
 6^{14}5^{13} -6^{13}5^{14}=

=6^{13}*5^{13}(6-5)=

=6^{13}*5^{13}=

=(6*5)^{13}=

=30^{13} 
 
Answer: E.

gmatophobia · Answer

-

(2*3*5)^{13}(6-5)

30^{13}

Option E

Jake7Wimmer · Answer

Bunuel  can you help with this question please

Elz068 · Answer

Could you explain this further to me? im not grasping the first step to the solution for some reason  Bunuel

Bunuel · Answer

We are simply factoring out  6^{13}*5^{13}  from  6^{14}5^{13} -6^{13}5^{14}  to get  6^{13}*5^{13}(6-5) .

RRINSEAD2025 · Answer

Bunuel,

This factorization is also confusing me a little. Aren't we meant to follow PEMDAS here?

I understand that almost always you're supposed to factorize subtracting or adding exponents, but here I'm not understanding how you reached 6^13 x 5 ^13 (6-5)

Thank you,

Bunuel · Answer

We’re not breaking PEMDAS here. The idea is just factoring out the common term.

From 6^14 * 5^13 - 6^13 * 5^14, notice both terms share 6^13 * 5^13.

First term = (6^13 * 6) * 5^13 
 Second term = 6^13 * (5^13 * 5)

So we can factor 6^13 * 5^13 out:

6^14 * 5^13 - 6^13 * 5^14 = 6^13 * 5^13(6 - 5).

It’s just standard factoring, not changing order of operations.

ablatt4 · Answer

2^x *5^x=10^x

6^x= (2*3)^x

(10^13*3^14*2)-(10^13#^13*5)

10^13*3^13(6-5)

10^13*3^13=30^13

E

(6^145^13) - (6^135^14) =

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