Question

What is the value of 5 to the power of 4 over 5 to the power of 6?

1 over 25
1 over 5
5
25

Answer 1

so\[5^{\frac{ 4 }{ 5^{6} }}\]?

Answer 2

5^4 over 5^6

Answer 3

5^4 is short hand for 5*5*5*5
and 5^6 is short for 5*5*5*5*5*5
can you simplify
\[ \frac{5\cdot 5\cdot 5\cdot 5}{5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5}\]?

Answer 4

4 over 6

Answer 5

do you remember how you multiply fractions? top times top and bottom times bottom
for example, we could write that as
\[ \frac{5}{5} \cdot \frac{5\cdot 5\cdot 5}{5\cdot 5\cdot 5\cdot 5\cdot 5}=\frac{5\cdot 5\cdot 5\cdot 5}{5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5} \]
(we could write it lots of ways, but notice if you multiply top times top and bottom times bottom you get 5^4/5^6

but notice, what is 5/5 ?

Answer 6

do you know that anything divided by itself is 1 ?

Answer 7

yes

Answer 8

wait so 1 over 2

Answer 9

if we wanted we could "break up" the fraction into lots of 5/5 fractions that multiply together. Each 5/5 turns into 1

**wait so 1 over 2**
almost, but it is 1/(5*5) (not 2)

Answer 10

If you have a 5 "up top" and a 5 "below" you have a 5/5 and that is 1
so you can "cancel" that pair.

Answer 11

If you get the idea that your problem is the *same* as
\[ \frac{5}{5} \cdot \frac{5}{5} \cdot \frac{5}{5} \cdot \frac{5}{5} \cdot \frac{1}{5\cdot 5} \]
and each 5/5 is 1
can you can simplify that ?

Answer 12

sorry just got back had to do something

Answer 13

1 over 5

Answer 14

in your problem
\[ \frac{5}{5} \cdot \frac{5}{5} \cdot \frac{5}{5} \cdot \frac{5}{5} \cdot \frac{1}{5\cdot 5} \]
change each 5/5 into 1 (because 5 divided by itself is 1)
now multiply it out
what do you get ?