Question

Can someone help me on this pls
Identify the property that is being applied at each step to simplify the expression

Answer 1

We are given

First expression:

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

We used property

power rule-II:

Product to power distribute  to each base

$(a \cdot b)^m=a^m \cdot b^m$

Second expression:

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

we used property

associative property of multiplication:

$a \cdot b \cdot c \cdot d =(a \cdot b) \cdot (c \cdot d)$

Third expression:

$=4^0 \cdot 9^2$

we used property

Product Rule:

Same base add exponents

$a^m \cdot a^n =a^{m+n}$

Fourth expression:

$=1 \cdot 9^2$

we used property

Zero Exponent :

Anything to the zero power  (except 0) is one

$a^0=1$

Fifth expression:

$= 9^2$

we used property

Multiplicative identity:

$1 \cdot a=a$

Sixth expression:

$= 81$

We used simplification