Question

(50 points) EXPRESS AS A POWER OF 3, Please explain your work

do a, b, and c
don’t troll or steal answers, i searched the answers up but nothing popped up :/

Answer 1

`\textsf{(a)} \quad 3^(-2)`

`\textsf{(b)} \quad 3^(-5)`

`\textsf{(c)} \quad 3^(9)`

Explanation:

Part (a)

Given:

`(1)/(9)`

Rewrite 9 as 3²:

`\implies (1)/(3^2)`

`\textsf{Apply exponent rule} \quad (1)/(a^n)=a^(-n):`

`\implies 3^(-2)`

Part (b)

Given:

`(3^(-4) \cdot 3^2)/(3^3)`

`\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c):`

`\implies (3^((-4+2)))/(3^3)`

`\implies (3^(-2))/(3^3)`

`\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c):`

`\implies 3^((-2-3))`

`\implies 3^(-5)`

Part (c)

Given:

`27^2 / 3^(-3)`

Rewrite 27 as 3³:

`\implies (3^3)^2 / 3^(-3)`

`\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):`

`\implies 3^6 / 3^(-3)`

`\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c)`

`\implies 3^((6-(-3)))`

`\implies 3^((6+3))`

`\implies 3^9`