Simplify and write the answers with positive exponents Simpl

Simplify and write the answers with positive exponents

Simplify and write the answers with positive exponents 6^-2 r^-3/2^3(r^-5)^3

Solution

6^-2r^-3/(2^3(r^-5)^-3

denominator : (2^3(r^-5)^-3) = 2^3(r^(-5*-3) = 2^3(r^15)

use the exponent propert : a^-x = 1/a^x

So, 6^-2r^-3/(2^3(r^-5)^-3 = 1/(6^2)(r^3)(8)(r^15)

Property: a^x*a^y = a^(x+y)

= 1/(288)(r^18)

= 1/288r^18