Question

How do you solve the highlighted problem?

Answer 1

these just teest your understanding or memory on the exponential rules
the rules for each are as follows
a.
`(x^m)(x^n)=x^(m+n)`
b.
`(x^m)/(x^n)=x^(m-n)`
c.
`x^(-m)= (1)/(x^m)`
d.
`(ab)^m=(a^m)(b^m)` and
`(x^m)^n=x^(mn)`


so

a.
`(x^3)(x^(-2))=x^(3-2)=x^(1)=x`
b.
`(y^5)/(y^(-2))=y^(5-(-2))=y^(5+2)=y^(7)`
c.
`4^(-1)= (1)/(4^1)= (1)/(4)`
d.
`(4x^2)^3=(4^3)((x^2)^3)` and
`(x^2)^3=x^(2*3)=x^(6)`
result is
`64x^6`