Question

How to solve this indices quest

Answer 1

I cannot see exactly what the question is asking, however, i wam going to assume that it is wanting you to reduce to its simplest form. To do this you must first understand two of the laws of exponents. One law is that the multiplaction of an exponentially represented number by another exponentially represented number with the same base. In this situation we add the exponents together. An example is:
(a^6) * (a)

Any number (in this situation i am talking about the lone (a)) when written by itself, can also be considered raised to the power of 1. So the example i just wrote can be rewritten:
(a^6) * (a^1)

We now add the exponents and get
(a^7)


The other law is If one exponent is raised by another exponent, then the exponents can be multiplied together. For example:
(a^-2)^-3

Int this you see that a is raised to the -2 power and then that in turn is raised to the -3 power. Since the -2 is raised to the -3 power, we can use the law of exponents to simplify this by multiplying the 2 exponents to get 6. So for this example the answer would be:
a^6

so for the question at hand:
(a^-2 * b)^-3 * (a * b^-7)

the simplest way to look at this is to use the very old math rule stating that parenthesis come first. So we can re write this:
(a^-2)^-3 * (b)^-3 * (a) * (b^-7)

Now to use the exponential law of raising an exponent to another power and get:
(a^6) * (b^3) * (a) * (b^-7)

to see the next step easier i will rewrite this
(a^6) * (a) * (b^-3) * (b^-7)

There are two different bases, so not all of this can be combined, however we can combine some to get its most simplest form. With the law of multiping same base exponential numbers, we have to add the exponents of numbers with the same base together.
(a^7) * (b^-10)

if i understood what you were asking, i Believe this would be your answer.

Answer 2

(a^6 b^-3) (ab^-7)
a^6 b^-10