HELP ALGEBRA! EXAM TOMORROW! QUESTION D E F! image in description

Where do I start?

Thank you Alan.  I assume that the image was too big before.  Andre has now introduced coding so that oversized images are shrunk to an appropriate size.

Thank you reinout.

Thank you Rosala.  Your explaination was really great.  There is one thing I would like to point out though.  Consider this question.

$$x\times x^3$$      I know that you know the answer is  $$x^4$$

But you said that $$x$$ has no index.  This is not right.  $$x$$ ha an 'invisable' index of 1.

I often talk about invisable things.  It often makes understanding easier.  So

$$x \times x^3=x^1\times x^3=x^{1+3}=x^4$$

Have a look at the properties of powers on the Formulary here: http://web2.0calc.com/formulary/math/algebra

All you need to know are some of the basic rules in algebra;

$$(x^a)^b = x^{a \times b}$$

$$x^a \times x^b = x^{a+b}$$

$$\frac{x^a}{x^b} = x^{a-b}$$

So for d

$$\frac{(x^5)^2 \times x^8}{(x^4)^4} = \frac{x^{10} \times x^8}{x^{16}} = \frac{x^{18}}{x^{16}} = x^2$$

for e

$$\frac{(x^2)^3 \times (y^4)^2}{xy^3 \times x^5} = \frac{x^6 \times y^8}{x \times y^3 \times x^5} = \frac{x^6 \times y^8}{y^3 \times x^6} = \frac{x^6}{x^6}\times \frac{y^8}{y^3} = 1 \times y^{8-3} = y^5$$

I can't see f because the 'top answers' part is blocking my view. 

Reinout 

here are the simple examples of the basic rules that alan showed ! these may help u understand the examples and are done separately not in the sum !

here we go !

1.a) a³ b⁵  x  a²b²

the rule to solve this is x^a * x^b = x^a+b 

ANS = a3 b5 x a2 b2

=a³⁺² b⁵⁺²

=a⁵b^{7   = ANS}

if there isnt any power on either of the variables then u dont plus anything for eg. n*n=n² !

or if there is on one and not on the other then ull do like this eg. n⁷ x n = n⁸

the answer came n⁸ becoz there was no power on the other n so we assume it as one and so 7+1 = 8 !

c)p⁴q⁶/p³q⁹

rule= x^a / x^b

=x^a-b

so ANS =p⁴q⁶/p³q⁹

=p^4-3 q^6-9

=p¹q³   = ANS

and so if there no power on any variable then use the same thing i told u before but remember it has to be - in place of + , thats obvio !

this is the third rule (x^a )^b

=x^a*b 

an eg not from ur pic but = (b⁵)²

= b^5*2

=b¹⁰

so these are the rules , use them to solve the problems ! BEST OF LUCK for the exam ! 

With these images if you right-click on them you can choose "open image in new tab".  In the new tab the image isn't obscured.

thanks alan ! 

This is an old thread that was mainly on dealing with negative indices.

It is definitely worth a look.

http://web2.0calc.com/questions/indices-especially-negative-indices

I'm crossing my fingers for you!