Algebra Problems

[paper merlin]

I'm stuck on a bunch of algebra questions.

[mighty drift]

@paper merlin

Let’s take a look on the top left one

What is your approach to it?

[paper merlin]

im thinking use the product of powers property. (x^a * x^b) = x^a+b maybe?

[mighty drift]

Well 512 = 2^what?

[paper merlin]

wait I messed it up, got my left and right wrong. for that expression, I honestly don't know where to start. with the pemdas rule it states to start in the parentheses. but I can't really simplify the equation in there too much

so I would move on to exponents and simplify those?

[mighty drift]

Well what is 32

It is a power of something

[paper merlin]

would that equal two? would I also put 10 in its prime factor form?

[mighty drift]

Yes

[mighty drift]

Why

It’s just 10-2

[paper merlin]

I'm not sure, my notes say to do that but i guess I don't have to. now I have to use other properties right?

[mighty drift]

Just dividing exponents

2^what = 512

[paper merlin]

2^9 = 512

[mighty drift]

Yes

So 512^(1/4)

= 2^(9/4)

What about 4

[paper merlin]

2^2 = 4

[mighty drift]

So 2^(2/8)

Or 2^(1/4)

Simplified

You know how to divide exponents?

[paper merlin]

I would subtract them right?

[mighty drift]

Yes

Then subtract normally

Whatever you get - 8

[paper merlin]

so it would be 2^8/4 (or 2) -(10-2) is the equation now?

[mighty drift]

2^(8/4) = 2?

But rest is correct

[paper merlin]

-4 ?

[mighty drift]

Is that the final answer

[paper merlin]

I'm pretty sure yes

[mighty drift]

Yea

[paper merlin]

SWEET THANK YOU

[mighty drift]

Do you need help with the others or are you good

Now

[paper merlin]

I would appreciate help yes!

[mighty drift]

Ok

[paper merlin]

I'm slow at this stuff so thank you for your time

[mighty drift]

Let’s go to middle

What squared = 144

[paper merlin]

12^2

[mighty drift]

Yes

What to the power of 5 = 243

To make it easier x^2 = (243)^(2/5) = 9

x^2 = 9

[paper merlin]

3^5 ?

[mighty drift]

Yes

12/3

=

4

[paper merlin]

wait I'm confused where does 12/3 come from

[mighty drift]

The square root and the root of 5

Reveal whole numbers

Making 12/3

[paper merlin]

so would the original equation turn into 12^2/3^5 ?

[mighty drift]

Then you take sqrt of top removing the square and fifth root of bottom removing the power of 5

[paper merlin]

ohhhh okay i get it now

[mighty drift]

So we have 4

4-5 = -1

What cubed = 64

[paper merlin]

4^3

[mighty drift]

Yes

16/4

-1 + 16/4

Is your answer

[paper merlin]

why would the division turn into + ?

[mighty drift]

The / is the division

You are adding the first result to the second result

Not dividing

[paper merlin]

ohhh right right that makes sense

[mighty drift]

Top right

Just multiplying exponents rules

[paper merlin]

wouldn't it be adding? the product of powers property. (x^a * x^b) = x^a+b maybe?

[mighty drift]

Yes

Just use that

[paper merlin]

(-7)^-2

[mighty drift]

Yea

[paper merlin]

cool cool, that one was simple LOL

[mighty drift]

Middle left

An exponent raised to an exponent is multiplication

Just multiply the exponents of both the 2 and 5

[paper merlin]

(1/6)^-4 this one?

[mighty drift]

No

(2^4)/(5^9)

[paper merlin]

ohh okay okay let me try

2^12 / 5^27 ?

[mighty drift]

Yes

[paper merlin]

yayyyy

[mighty drift]

Ok

[paper merlin]

thank you for helping me this really means alot 😭

[mighty drift]

This one

Do you know what negative exponents do

?

[paper merlin]

do I use the reciprocal of it? turn it into a positive number by making it a fraction?

[mighty drift]

Yes

[paper merlin]

so it would turn into 1/4?

[mighty drift]

No

The 1/6

Would be reciprocal

So now 6

[paper merlin]

ohhh so I can use that on a base number and an exponent?

[mighty drift]

(1/6)^-4

= (6)^4

[paper merlin]

okay okay it's making sense, that would be the answer?

[mighty drift]

Yea

But you need a single integer

[paper merlin]

how would I get a single integer out of that?

[mighty drift]

6 * 6 * 6 * 6 = 6^4

36 * 36

[paper merlin]

1296? or would it just be 36?

[mighty drift]

1296

For middle right

Just use the same concept as the previous multiplying exponents one

[paper merlin]

would I need to find a common denominator first?

[mighty drift]

Yea

But it’s easy

3 and 4 denominator does not take long to find

[paper merlin]

12?

[mighty drift]

Yea

Want to know a neat trick?

[paper merlin]

7^12/12 or just 1

for sure

[mighty drift]

If you have two fractions (a/b) and (c/d)

Their sum is (ad + bc)/bd

In this case it’s 11/12

Not product

Oops

[paper merlin]

cool :0 I see that in the equation I just did now

how did I get 12/12?

[mighty drift]

So 7^(11/12)

Idk

Silly mistake probs

[paper merlin]

probably

[mighty drift]

Bottom left

Just use dividing exponent rules

[paper merlin]

would I find common denominator again?

[mighty drift]

1/4 = something/8

Then just subtract the two fractions

[paper merlin]

I'm confused a little bit

would it be 2/8?

[mighty drift]

1/4 = 2/8

[paper merlin]

and then 1/8

[mighty drift]

7/8 - 2/8

= ?

[paper merlin]

5/8 so
4^5/8

[mighty drift]

Yea

[paper merlin]

cool cool

this was so hard by myself but now that ur explaining it makes more sense

[mighty drift]

Next one is distributive property

[paper merlin]

so 8^3/4 * 3^5*3/4 ?

[mighty drift]

Yes

I would advise to put parenthesis in the 5 * 3

Because I know what you’re saying

But that is technically incorrect

[paper merlin]

okay okay noted for next time

would I add the exponents 3/4 and 15/4 together?

[mighty drift]

No

[paper merlin]

wait but they don't have the same base

[mighty drift]

Last one is again distributive property

[paper merlin]

oh okay so
my answer is
8^3/4 * 3^3/4

[mighty drift]

Huh

Where did the 5 go

[paper merlin]

because I got 3^15/20 which would simplify to 3/4, no?

when I multipled the 5 * 3/4

[mighty drift]

5 * 3/4 = 15/4

[paper merlin]

ohhh okay okay

ohhhh I see what I did wrong

multipled the top and bottom oops

[mighty drift]

Just do this to solve last one

[paper merlin]

would it be
9^9/5 / 5^9/10 ?

[mighty drift]

Yea

[paper merlin]

yay!! thanks so much for your help.