Question

1. vocabulary identify the property that is being applied at each step to simplify the expression.

4^{-5}cdot(4cdot9)^{5}cdot9^{-3}=4^{-5}cdot(4^{5}cdot9^{5})cdot9^{-3}
=(4^{-5}cdot4^{5})cdot(9^{5}cdot9^{-3})
=4^{0}cdot9^{2}
=1cdot9^{2}
=9^{2}
=81

Explanation:

Step1: Apply product - power property

$4^{- 5}\cdot(4\cdot9)^{5}\cdot9^{-3}=4^{-5}\cdot(4^{5}\cdot9^{5})\cdot9^{-3}$

Step2: Apply commutative property of multiplication

$4^{-5}\cdot(4^{5}\cdot9^{5})\cdot9^{-3}=(4^{-5}\cdot4^{5})\cdot(9^{5}\cdot9^{-3})$

Step3: Apply product - of - powers property ($a^{m}\cdot a^{n}=a^{m + n}$)

$(4^{-5}\cdot4^{5})\cdot(9^{5}\cdot9^{-3})=4^{-5 + 5}\cdot9^{5+( - 3)}=4^{0}\cdot9^{2}$

Step4: Apply zero - exponent property ($a^{0}=1,a

eq0$)
$4^{0}\cdot9^{2}=1\cdot9^{2}$

Step5: Simplify

$1\cdot9^{2}=9^{2}$

Step6: Calculate the square

$9^{2}=81$

Answer:

81