Question

Medal Q10
http://prnt.sc/cisg8s

Answer 1

@mathstudent55 @mathmale @ltrout

Answer 2

compute \[4^{-3}*4^2~first.\]

Answer 3

Review rules of exponentiation. 4^a*4^b =4^(a+b)

Answer 4

Adapt this rule to fit the current situation.

Answer 5

what is 4^-3?

Answer 6

Your 4^-3, better written as \[4^{-3},\] is equal to \[\frac{ 1 }{ 4^3 }. \]

Answer 7

What is 4^3?

Answer 8

64?

Answer 9

yes.

Answer 10

But in the numerator of the given problem, you have \[4^{-3}4^2\] Please reduce this.

Answer 11

Combine the 2 exponents, -3 and +2. Write your result here:

Answer 12

3882 @mathmale

Answer 13

@mathmale @WHEREISTHEFLOOR @Elsa213 @TheSmartOne @AloneS

Answer 14

what is the problem it looks like mathmale solved it

Answer 15

Go back and look at the original problem, please.

I asked that you simplify:\[4^{-3}4^2\]

Answer 16

using the appropriate rule of exponentiation.

Answer 17

Here are 2 such rules:\[a^b a^c=a ^{b+c}\]

Answer 18

\[e^c e ^{-d}=e ^{c-d}\]

Answer 19

i dont get that

Answer 20

8^-1?

Answer 21

As before, there are "rules of exponentation" that you MUST learn, study and apply to problems. It's not a matter of "I don't get that;" you have to learn this material and remember it for later application.

Answer 22

\[4^{-3}4^2\] reduces to \[4^{-3+2}\]

Answer 23

Note that we kept the base 4 here; do NOT change the base. Again, follow the rules of exponentiation.

Answer 24

ok

Answer 25

Now, please reduce / simplify:\[4^{-3+2}\]

Answer 26

What is -3+2?

Answer 27

@mathmale -1

Answer 28

Right. Now, please evaluate / simplify\[4^{-1}\]

Answer 29

well since 4^1 is 1 would this be -1?

Answer 30

Milo, it appears you'll need to read up on "exponentiation." That \[4^{-1}\]

Answer 31

consists of the base, 4, and the exponent, -1.

The pertinent rule is \[a ^{-1}=\frac{ 1 }{ a^1 }=\frac{ 1 }{ a }\]

Answer 32

You must know and understand this rule.

Answer 33

Using this rule, find the value of\[4^{-1}\]

Answer 34

Note that this is not a multiplication problem; it's an exponentiation one.

Answer 35

\[\frac{ 1 }{ 4^1 }\]