simplify: 1. a^2b^-3 2. (5/3)^-3 3. (a^2b^0c)^0 4. x^-2y^3 5. 3x^-2 6. n^2/n^-3 please help!!

for (1),

a^2 * b^(-3)
note that when a term is raised to a negative exponent, we get its reciprocal and raise it by the positive exponent,, for example,
2^(-4) = 1/(2^4) ; thus we can rewrite
b^(-3) = 1/(b^3)
therefore,
a^2 * (1/(b^3))
a^2 / b^3

for (2),
(5/3)^-3
we do the same thing,, get the reciprocal, make the exponent positive and simplify:
(3/5)^3
27 / 125

for (3),
(a^2b^0c)^0
note that any number (except zero) raised to zero is equal to 1,, thus assuming a, b and c are not equal to 0,
(a^2b^0c)^0 = 1

for (4),
do you mean x^(-2) * y^(3) ? if so,
it's the same as #1:
(1/(x^2)) * y^3
y^3 / x^2

for (5),
3x^-2
it's also the same procedure as #1:
3*(1 / (x^2))
3/(x^2)

for (6),
(n^2) / (n^(-3))
same procedure as #1,,
(n^2) / (1/(n^3))
simplifying,
(n^2)*(n^3)
note that when multiplying terms raised to exponents but have the same base, we can just add the exponents,, for example
2^3 * 2^5 = 2^(3+5) = 2^8
note that the base here is 2.
therefore,
(n^2)*(n^3) = n^(2+3) = n^5

hope this helps~ :)

thanks! i really appreciate this :)

Sure, I'd be happy to help you simplify these expressions!

1. To simplify 1. a^2b^-3, remember that a negative exponent means taking the reciprocal of the base. So, b^-3 is the same as 1/b^3. Thus, the expression becomes a^2 / b^3.

2. To simplify 2. (5/3)^-3, we can apply the negative exponent directly to the fraction within the parentheses. This means we need to reciprocate the whole fraction. Therefore, (5/3)^-3 becomes (3/5)^3.

3. To simplify 3. (a^2b^0c)^0, any base raised to the power of zero always equals 1. So, (a^2b^0c)^0 simply becomes 1.

4. To simplify 4. x^-2y^3, we can apply the negative exponent to x and the positive exponent to y. x^-2 becomes 1/x^2. Therefore, the expression becomes 1/x^2 * y^3, or y^3/x^2.

5. To simplify 5. 3x^-2, we can apply the negative exponent to x. x^-2 becomes 1/x^2. Thus, the expression becomes 3 / x^2.

6. To simplify 6. n^2/n^-3, we can divide the terms with the same base by subtracting their exponents. n^2/n^-3 becomes n^(2 - (-3)), which is n^5.

So, the simplified expressions are:
1. a^2 / b^3
2. (3/5)^3
3. 1
4. y^3/x^2
5. 3 / x^2
6. n^5