Question

Match each power of a power expression with its simplified expression.

(4-3)-3
(46)-3
(49)-9
(-49)²
↑
↑
1
418
49
(-4)18
40
need to know which one goes to which

Answer 1

(4^6)^-3 = 1/4^18(4^0)^-9 = 4^0(4^-3)^-3 = 4^9(-4^9)^2= (-4)^18Step-by-step explanation:(4^6)^-3 = 1/4^18(4^6)^-3= 4^(6*-3)(4^6)^-3= 1/4^18(4^0)^-9 = 4^0(4^0)^-9 = 4^(0*-9)(4^0)^-9= 4^0(4^-3)^-3 = 4^9(4^-3)^-3= 4 ^ (-3*-3)(4^-3)^-3 = 4^(9)(-4^9)^2= (-4)^18(-4^9)^2= -4^(9*2)(-4^9)^2=(-4)^18

Explanation:

Answer 2

`(4^(-3))^(-3)=4^9`

`(4^6)^(-3)=(1)/(4^(18))`

`(4^0)^(-9)=4^0`

`(-4^9)^2=(-4)^(18)`

Explanation:

`\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$(a^b)^c=a^(bc)$\\\\$a^(-n)=(1)/(a^n)$\\\end{minipage}}`

Apply the above exponent rules to simplify each expression.

`\begin{aligned}\implies (4^(-3))^(-3)&=4^(-3 * -3)\\&=4^9\end{aligned}`

`\begin{aligned}\implies (4^6)^(-3)&=4^(6 * -3)\\&=4^(-18)\\&=(1)/(4^(18))\end{aligned}`

`\begin{aligned}\implies (4^0)^(-9)&=4^(0 * -9)\\&=4^0\end{aligned}`

`\begin{aligned}\implies (-4^9)^2&=(-4)^(9 * 2)\\&=(-4)^(18)\end{aligned}`