Answer:
Please check the explanation!
Step-by-step explanation:
Given the expression what Lizzet said was correct
[tex]6^3\times \:\:3^6=18^8[/tex]
No, she is not right. Let me solve the expression
Let us solve the expression
[tex]6^3\times \:\:3^6[/tex]
[tex]=\left(3\times \:2\right)^3\times \:3^6[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\:\:\:\left(ab\right)^c=a^cb^c[/tex]
[tex]=3^3\times \:2^3\times \:3^6[/tex] ∵ [tex]\left(3\times \:2\right)^3=3^3\times \:2^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\:\:a^b\times \:\:a^c=a^{b+c}[/tex]
[tex]=2^3\times \:3^{3+6}[/tex] ∵ [tex]3^3\times \:3^6=\:3^{3+6}[/tex]
[tex]=2^3\times \:3^9[/tex]
Therefore, the correct expression will be:
[tex]6^3\times \:\:3^6=2^3\times \:\:3^9[/tex]
which can be further simplified such as:
[tex]6^3\times \:\:3^6=2^3\times \:\:3^9[/tex]
[tex]=8\times \:19683[/tex]
[tex]=157464[/tex]
