Question

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

Answer 1

Answer:

> $(4^6)^{-3}$ = $\frac{1}{4 ^ {18}}$

> $(4^{-3})^{-3}$ = $4 ^ 9$

> $(4^0)^{-9}$ = $4 ^0$

> $(-4^{-9})^2$ = $(-4) ^ {-18}$

Step-by-step explanation:

We have to expand the powers of each of them:

> $(4^6)^{-3}$ = $4^{(6 * -3)}$

          = $4 ^ {-18}$

$(4^6)^{-3}$ = $\frac{1}{4 ^ {18}}$

> $(4^{-3})^{-3}$ = $4 ^ {(-3 * -3)}$

  $(4^{-3})^{-3}$ = $4 ^ 9$

> $(4^0)^{-9}$ = $4 ^ {(0 * -9)}$

  $(4^0)^{-9}$ = $4 ^0$

> $(-4^{-9})^2$ = $-4 ^ {( -9 * 2)}$

  $(-4^{-9})^2$ = $-4 ^ {-18}$

Answer 2

Answer:

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

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

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

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

Step-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