What is the missing value?

A.
−13

B.
−5

C.
5

D.
13

Question

What is the missing value?
 
 
 
 A.
−13
 
 B.
−5
 
 C.
5
 
 D.
13

brucebaner · Answer

danjs · Answer

recall...

danjs · Answer

$$\frac{ 8^a }{ 8^b } = 8^{a - b}$$

brucebaner · Answer

can you help me @DanJS and @cwrw238

danjs · Answer

something + 4 = 9

danjs · Answer

a = not known
b = -4

a - b  = a-(-4) = a+ 4 = 9

a + 4 = 9

brucebaner · Answer

so that letter is it is it C

danjs · Answer

yep

brucebaner · Answer

thx

brucebaner · Answer

is it C @Michele_Laino

danjs · Answer

$$\frac{ 8^a }{ 8^{-4} } = 8^{a -(-4)} = 8^{a+4} = 8^9$$

danjs · Answer

since it is the same base, you can equate the powers

a + 4 = 9

brucebaner · Answer

okay thx

danjs · Answer

just remember when you move a base to a power to the opposite side of a fraction... you switch the sign on the power, + to - or - to +

michele_laino · Answer

@brucebaner  please follow the good reasoning of @DanJS , solve the equation a+4=9
for a

brucebaner · Answer

thx so much @Michele_Laino and @DanJS

danjs · Answer

your welcome, anytime

michele_laino · Answer

thanks! @brucebaner