Are the following correct? Simplify. 1. 10^-4 = 1/10000 2. a^2 b^-3 = ab^-1 3. (5/3)^-3 = 27/75

To understand negative exponents one must understand the
rules of fractions and operations of exponents.

First: any
number or expression can be represented as a fraction with a denominator of
1.

A negative exponent is telling us to take the fraction
to which it is being applied and rewrite it as its inverse ("flip it over").  The
exponent then becomes positive.  Any other operations signified by the exponent are then
applied.  Keep in mind, if the exponent is outside of a set of parenthesis, it is
applied to what is inside; if it is applied to an expression without parenthesis it
affects only the factor to its immediate left.

For
example:

``

and

`x^-2
= 1/x^2`

We can apply these to the expressions from above
to determine their correctness:

1.  `10^-4 = 1/10^4 =
1/10*10*10*10 = 1/10000`

2.  `a^2 b^-3 = a^2/1 * 1/b^3 =
a^2/b^3`

3.  `(5/3)^-3 = (3/5)^3 = 3^3/5^3 =
(3*3*3)/(5*5*5) = 27/125`