Question

I have the answers .. but can someone explain how to get them? Thank you xx

Answer 1

So you have to solve for \(x\) then?

Answer 2

d. x=1.69
e.x=3.68
f. x=42.88
g. x=32
h. x=18.99
i=58.72

Answer 3

yes the directions say to solve for x

Answer 4

You have to change the expression into a simple fractional exponent. Something of the form \(x^{a/b}\). Then you take both sides to the power of \(b/a\). This will isolate \(x\).

Answer 5

for example for d what would I raise?

Answer 6

For \(d\), we can see \[
\frac{1}{\sqrt{x}} = \frac{1}{x^{1/2}}=x^{-1/2}
\]Now the reciprocal of \(-1/2\) is going to be \(-2/1 = -2\).

Answer 7

Thus \[
\left(\frac{1}{\sqrt{x}}\right)^{-2}=x=(0.77)^{-2}

\]

Answer 8

ok I see now :) thanks so much so for e what would i have to do since theres 8 in the root

Answer 9

Use \[
\sqrt[b]{x^a} = x^{a/b}
\]

Answer 10

Remember that \(\sqrt{x} = \sqrt[2]{x}\)

Answer 11

You also need to use \(\frac{1}{x^a}=x^{-a}\)

Answer 12

so -2/3?

Answer 13

Well, there is no negative in d.

Answer 14

whoops, I mean no negative in e. We had one in d because it was a fraction.

Answer 15

I don't really understand how to do e. I looked at the rules but I didn't understand :/

Answer 16

Okay for e, we have to do it one at a time.

Answer 17

\[
\sqrt{8x^3}=(8x^3)^{1/2}
\]So first we do both sides to the power of \(2\).

Answer 18

\[
8x^3 = (20)^2 = 400
\]

Answer 19

Then we divide by \(8\): \[
x^3= 400/8=50
\]

Answer 20

Now we do reciprocal of \(3\) which is \(1/3\) \[
x = (50)^{1/3}
\]

Answer 21

oh ok i see now:))) so for f-i are they the same method?

Answer 22

Yes.

Answer 23

When you isolate the variable, you generally get rid of things opposite of the order of operations. Thus exponents are the last part to get rid of.

Answer 24

for f is would be 1/3 since we don't touch the exponent?

Answer 25

What do you mean?

Answer 26

because i think you would need to subtract 18 and 32 -18 is 14 so i'm kinda stuck from there

Answer 27

Yes, then you get rid of the \(4\) next.

Answer 28

Then you can get rid of the power after that.

Answer 29

to get rid of the 4 can i just divide it or do i do the reciprocal?

Answer 30

You are dividing. Which is actually the same as multiplying by the reciprocal.

Answer 31

You can divide by \(4\) or multiply by \(1/4\). Both work.

Answer 32

how would the power of 3 work though

Answer 33

Well, you have \(x^{1/3}\). The reciprocal is \(3\).

Answer 34

but 14 to the exponent of 1/3 isn't 42.88 that's where i'm kinda lost

Answer 35

it's just the 1/4 and the 1/3 are confusing me

Answer 36

lmao @lilliegirl's profile pic looks like the pic from the song "marl1"

Answer 37

lool

Answer 38

does anyone know how to do f? I'm seriously stuck

Answer 39

\[4\sqrt[3]{x}+18=32\]Subtract 18 from both sides.\[4\sqrt[3]{x}=14\]Divide both sides by 4.\[\sqrt[3]{x}=\frac{7}{2}\]Raise both sides to the 3rd power.\[x=(\frac{7}{2})^3 \]

Answer 40

Or if you prefer:
\[4\sqrt[3]{x} = 14\]Raise both sides to 3rd power.\[64x=2744\]\[x=\frac{343}{8}\]

Answer 41

thank you so much for helping everything.. I really appreciate it!