We are given
First expression:
[tex]4^{-5} \cdot (4 \cdot 9)^{5} \cdot 9^{-3}=4^{-5} \cdot (4^{5} \cdot 9^{5}) \cdot 9^{-3}[/tex]
We used property
power rule-II:
Product to power distribute to each base
[tex](a \cdot b)^m=a^m \cdot b^m[/tex]
Second expression:
[tex]=(4^{-5} \cdot 4^{5}) \cdot ( 9^{5}) \cdot 9^{-3})[/tex]
we used property
associative property of multiplication:
[tex]a \cdot b \cdot c \cdot d =(a \cdot b) \cdot (c \cdot d)[/tex]
Third expression:
[tex]=4^0 \cdot 9^2[/tex]
we used property
Product Rule:
Same base add exponents
[tex]a^m \cdot a^n =a^{m+n}[/tex]
Fourth expression:
[tex]=1 \cdot 9^2[/tex]
we used property
Zero Exponent
:
Anything to the zero power (except 0) is one
[tex]a^0=1[/tex]
Fifth expression:
[tex]= 9^2[/tex]
we used property
Multiplicative identity:
[tex]1 \cdot a=a[/tex]
Sixth expression:
[tex]= 81[/tex]
We used simplification
