What level is this question in the maths curriculum?

[essex-mum18]

Find the value of a and b in the following question.

2 to the power of a x 5 to the power of b =200

I use prime factorization to work out 2x2x2x5x5, therefore the value of a =3 and the value of b=2

I wonder what level would you expect this sort of question in the exam? Thanks in advance.

[SunlampVexesEel]

I can't answer the question on level... we'll have to wait for a teacher to do that...

... but... it does seem pretty simple... i.e even if you don't factor it... there is an obvious 25x8 there. Factoring, given that 2 and 5 are prime, of course is the correct approach.

I'll try it out of the DCs later

Regards
SVE

[Guest55]

About a level 7 -ish

[dadofkent]

Surely it is simpler than that. It cannot be 5 cubed because that will give 125, therefore it has to be 5 squared. The rest follows.

QED

[Guest55]

It's hard to judge because the full question hasn't been quoted - if it's all written in algebraic form it makes it harder.

[Bewildered]

and this one, pls...

1/x=3/4

What is the value of x?

[hermanmunster]

er bit late - back from work and out with the beer ....

1/x=3/4
multiply through by x -> 1=3x/4
multiply through by 4 -> 4=3x
divide through by 3 -> 4/3=x
x= 4/3 or 1.33333333333333333333333

- oops there's a simpler way I've just realised

[Bewildered]

Thanks Herman, that's what I made it. But confusion is, are you allowed to make the denominator a mixed number???

[hermanmunster]

now I'm feeling bewildered!!! what's a mixed number?

[Bewildered]

sorry, I meant a whole number part and a decimal/fraction part like 1.33, by mixed number.

Normally you'd only have a whole number as a denominator. (well in the lower types of maths I've done, you do )