Answer:
[tex]2^{100}[/tex]
Step-by-step explanation:
Given expression:
[tex]2^{40} \times 4^{30}[/tex]
Rewrite 4 as 2²:
[tex]\implies 2^{40} \times (2^2)^{30}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 2^{40} \times 2^{(2\times30)}[/tex]
[tex]\implies 2^{40} \times 2^{60}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 2^{(40+60)}[/tex]
[tex]\implies 2^{100}[/tex]
Therefore, n = 100.
