Answer:
[tex]6^7[/tex]
Step-by-step explanation:
[tex]9^2(12^3)(2)[/tex]
[tex]\mathsf{rewrite \ 9 \ as \ 3^2 } \implies 9^2=(3^2)^2[/tex]
Apply exponent rule [tex](a^b)^c=a^{bc}[/tex]:
[tex]\implies (3^2)^2=3^4[/tex]
[tex]\mathsf{rewrite \ 12 \ as \ 2 \cdot 2 \cdot 3 } \implies 12^3=(2 \cdot 2 \cdot 3)^3[/tex]
Apply exponent rule [tex](a\cdot b)^c=a^c \cdot b^c[/tex]
[tex]\implies (2 \cdot 2 \cdot 3)^3=2^3 \cdot 2^3 \cdot 3^3[/tex]
[tex]\mathsf{rewrite \ 2 \ as \ 2^1}[/tex]
Therefore,
[tex]9^2(12^3)(2)=3^4 \cdot2^3\cdot2^3\cdot3^3\cdot2^1[/tex]
Gather like terms
[tex]\implies 3^4\cdot3^3 \cdot2^3\cdot2^3\cdot2^1[/tex]
Apply exponent rule [tex]a^b \cdot a^c=a^{b+c}[/tex]:
[tex]\implies 3^{4+3}\cdot2^{3+3+1}[/tex]
[tex]\implies 3^7 \cdot 2^7[/tex]
Apply exponent rule [tex]a^c \cdot b^c=(ab)^c[/tex]
[tex]\implies (3 \cdot2)^7[/tex]
[tex]\implies 6^7[/tex]
