Simplifying an equation? (q^-3)^-2?

(q^-3)^-2

when you have par ens you multiply the exponents
(-3)(-2) = 6

so the answer is q^6


If you write it this way
never leave your exponent negative in your final answer
(1/q^3)^-2 = 1/q^-6 = q^6

hope this helps!!!

you can rewrite this as 1/(q^3)^2
now you can multiply the exponents to get an answer of 1/q^6

First note that you have a term (q) raised to a power (^-3) all of which is then raised to another power (-2). This is simplified using one of the rules of indices:

(a^n)^m = a ^(n*m) so for your expression we get:

q^(-3*-2) = q^6

Note here that (-) times a (-) gives a (+). A good way to check this sort of simplification is to choose a value for q and do the two calculations with a calculator. For example, let q = 2, then:

(2^-3)^-2 = 64 and 2^6 = 64 as required.

q^(a)^b = q^(ab)
q^(-3)^(-2) = q^6

in this case the base is the same but you just need to multipling the exponents
so the answer is q^-6

the answer is q to the 2nd power as the 1st and 3rd users replied. the 2nd user was correct in her reasoning that a negative exponent can be canceled into a fracture of one, but forgot that two negatives were involved, whos fractures would cancel eachother to create the same exact answer: q to the 2nd power.

First, you know q^-3 can be written as 1/q³.

Also, (1/q³)^-2 can be written as 1/[(1/q³)²]

(1/q³)² can be written as 1/q^6 because you're squaring everything so your fraction becomes:

1/(1/q^6)

To divide a fraction, you multiply by its reciprocal (upside down of a fraction).

The reciprocal of (1/q^6) is q^6

Therefore, 1 * q^6

Your answer is q^6

(q^-3)^-2
= q^(-3 * -2)
= q^(6)
= q^6