#56 (x-4/7)^7

Hello CPhil!

I still think you should get paid to do this stuff! And i am also deeply sorry if any of these are "vague"? I am strictly going by what is in the book. I do not make them up.

There are many solutions, Nataszaa.

#56 (x-4/7)^7

I will solve this one, okay?

Substitute x.

$${\mathtt{x}} = {\mathtt{2}}$$

In this case, $${\mathtt{x}} = {\mathtt{2}}$$.

Now, turn 2 into a fraction.

$${\mathtt{2}} = {\frac{{\mathtt{2}}}{{\mathtt{1}}}}$$

Now, subtract.

$${\frac{{\mathtt{2}}}{{\mathtt{1}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{4}}}{{\mathtt{7}}}} = {\frac{{\mathtt{10}}}{{\mathtt{7}}}}$$

But now, turn $${\frac{{\mathtt{10}}}{{\mathtt{7}}}}$$ into a whole number.

$${\frac{{\mathtt{10}}}{{\mathtt{7}}}} = {\mathtt{1.428\: \!571\: \!428\: \!571\: \!428\: \!6}}$$

Now, that you have the whole number, round it to the nearest tenths.

$${\mathtt{1.428\: \!571\: \!428\: \!571\: \!428\: \!6}} = {\mathtt{1.4}}$$

Now, do the exponent $${{\mathtt{1.4}}}^{{\mathtt{7}}}$$.

$${{\mathtt{1.4}}}^{{\mathtt{7}}} = {\mathtt{10.541\: \!350\: \!4}}$$.

That's your answer.

Now, I will do this one.

#57 (3x 2/3)^7-6

Substitute x.

$${\mathtt{x}} = {\mathtt{1}}$$

Now, multiply.

$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{1}} = {\mathtt{3}}$$

Now, subtract.

$${\mathtt{7}}{\mathtt{\,-\,}}{\mathtt{6}} = {\mathtt{1}}$$

Now, the whole question together.

$$(3\frac{2}{3})^1$$

Now, finish the expression.

$$(3\frac{2}{3})^1=3\frac{2}{3}$$

So, $$3\frac{2}{3}$$ is the answer.

#57

(3x 2/3)^7-6

You need to learn to use brackets Nataszaa,  we can't read you mind. 

Plus, you can't really have a letter followed by a number - it doesn't make sense. Sorry.

$$\\\mbox{Do you mean:}\\\\
\left(\frac{3x\times2}{3}\right)^7-6\\\\
\left(\frac{3x^2}{3}\right)^7-6\\\\
(3x^{2/3})^7-6\\\\
\mbox{or something else? }$$

Since some of these seem to be the application of the exponent rule .... (a^b)^c = a^bc ... I'm assuming that 56 might be:

(x^-4/7)⁷ =

x^-4

We can only guess, at this point.....!!!

@Melody

These questions are from a book...i did not make them up so...i cannot read the books mind either. 

THANK YOU FOR ANSWERING THESE 2

can someone do the other 3?

#58 5(x2/3)^7-6

I'm assuming that we have this???......... 5[x^(2/3)]^(7-6)   = 5[x^(2/3)]^(1) = 5[x^(2/3)] = 5x^(2/3).......I'm not too sure that I've answered what was actually asked on this one, Nataszaa !!!! If it's not....maybe you could provide more info to us ????

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#59 (-27x^-9)1/3

So we have....

-3x^(-3)

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#60 (-32y^15)1/5

So we have....

-2y^3

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And that's it!!!

I didn't think that you were making them up Nataszaa.  But I think the book presents them in 'math speak' and when you interprete them into 'keyboard presentation' it is sometimes difficult to get the brackets etc in the correct places.

The book would not have presented it like this

#57 (3x 2/3)^7-6

Something is missing.  

I did give you 3 interpretations to choose from but you didn't say which was the correct one.  

Dragon Slayer 

When you are doing questions like this you cannot just say x=1 or x=2.

It doesn't work quite that way  

I might try and find you some questions that you can answer legitimately and maybe learn something too.

Would you like that?