Question

^ = to the power

1. 8^1/2*8^-5/2
2.3^5/3(divided by) 3^2/3

**please show work

Answer 1

to multiply add exponents if the base is the same
8^(1/2 -5/2)
= 8^(-2)
= 1/8^2
= 1/64

1/3^(2/3) = 3^(-2/3)
so
=3^(5/3) * 3^(-2/3)
=3^(3/3)
=3

Answer 2

i do not understand the second problem.

Answer 3

negative exponent definition:

a^-b = 1/(a^b)

derivation:

when you multiply you add exponents
when you divide you subtract exponents (remember a^0 = 1)
1/a^b = a^0/a^b = a^(0-b) = a^-b