Evaluating Numerical Expressions problem help?

Question

Got stuck on this problem please help if you can!

6^2
-----------------
(6^-2 * 5^1)^-2

Please show all work!

Answer 1

Start with the bottom. Since the whole thing is to the -2 power, you can bring it all up to the top.

6^2 * (6^-2 * 5^1)^2

Now on the inside, 6^-2 is 1/6^2, and 5^1 is just five, so that simplifies to (1/6^2 * 5) or (5/6^2)

So now the problem is 6^2 * (5/6^2)^2

Distribute the ^2 to the 5 and the 6^2. Remember, a power to a power means to multiply.

6^2 * (5^2/6^4)

Now look at the 6^2 and the 6^4. Two of the powers cancel eachother out (when the bases are the same, the powers add when you multiply and subtract when you divide).

so 6^2/6^4 = 1/6^2. keep the 5^2 and the final answer is

5^2/6^2, or 25/36.

Answer 2

(6^2) / (6^[-2] * 5^(1))^(-2)

First, distribute the (-2) power through the brackets. Remember that we apply -2 to each term inside the brackets.

(6^2) / { [6^(-2)]^(-2) * [5^1]^(-2) }

Remember that whenever we have a power to a power, we multiply exponents.

(6^2) / { [6^4] * [5^(-2)] }

Now, we can actually cancel stuff out. Note that the 6^2 on the top and the 6^4 on the bottom will cause some cancellation. The 6^2 will disappear (leaving behind a 1), and the 6^4 will have its power reduced by 2.

1/[5^(-2)]

Note that whenever we take a base to a power across the division sign, the exponent switches sign.

5^2

Which is

25

Answer 3

6^2(1/6^2*5)^2
=36*25/36*36
=25/36

Answer 4

6^2
-----------------
(6^-2 * 5^1)^-2

The numerator is 6^2 = 36
The denominator is (1/36 *5)^-2 = (5/36)^-2 = 1/(5/36)^2
= 36^2/5^2
So, 36/(36^2/5^2) = (36* 5^2)/ 36^2 = 5^2/36 = 25/36

Answer 5

30 "branch sign is going right here" 5 "domulitilpulcation t is going right here" 7 -5^3 Presuming it’s something like this 30/5 ? 7 - 5³ With no longer something better to bypass on, 30/5 ? 7 - 5³= 6 ? 7 – one hundred twenty five = 40 two – one hundred twenty five = -eighty 3

Answer 6

lets break this down into segments:

6^2 = 36
-------------------
6^-2 = 1/36
5^1 = 5

so:
36
---------------- =
(1/36 * 5)^-2


36
------------- =
(5/36)^-2


36
-------------- =
1
-----
25
----
1296


36
----------- =
1296
-----
25


25 * 36
---------- =
1296


900
------- =
1296

simplyfied (divide both the top and bottom by 36)
25
----- <=== answer
36