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