Question

There are (3^2)^4 ⋅ 3^0 bacteria in a Petri dish. What is the total number of bacteria in the dish?

Answer 1

@iGreen

Answer 2

Simplify the exponent inside the parenthesis.

\(\sf 3^2=~?\)

Answer 3

9

Answer 4

Correct, now simplify:

\(\sf (9)^4\)

Answer 5

6561?

Answer 6

Yep!

And what's \(\sf 3^0\)?

Answer 7

1

Answer 8

Correct, that leaves us with:

\(\sf 6561\times 1\)

Answer 9

6561

Answer 10

they may want the answer as
\[ 3^8\]

you can find this answer by knowing something to the 4th power means multiply by itself four times, so
\[ \left(3^2\right)^4= 3^2\cdot 3^2 \cdot 3^2\cdot 3^2\]
you should know \( 3^2= 3 \cdot 3\)
so you can also write this as
\[ 3^2\cdot 3^2 \cdot 3^2\cdot 3^2= 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \]
use the "short way" to show you have 3 multiplied by itself 8 times

Answer 11

in other words
\[ 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3=3^8\]

Answer 12

okay thank you that is what my question asked for

Answer 13

Yes, @phi is just explaining another way to do it.

\(\sf 3^8\) also gives us the answer of 6561

Answer 14

Nice work

Answer 15

ok thanks