Question

Express 2^40 × 4^30 in the form 2^n​

Answer 1

`2^(100)`

Explanation:

Given expression:

`2^(40) * 4^(30)`

Rewrite 4 as 2²:

`\implies 2^(40) * (2^2)^(30)`

`\textsf{Apply exponent rule} \quad (a^b)^c=a^(bc):`

`\implies 2^(40) * 2^((2*30))`

`\implies 2^(40) * 2^(60)`

`\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c):`

`\implies 2^((40+60))`

`\implies 2^(100)`

Therefore, n = 100.