Question

4.8 * 10^24 - 7.9 * 10^25 in exponential form

Answer 1

-7.42 × 10²⁵

Explanation:

Given expression:

`4.8* 10^(24)-7.9 * 10^(25)`

Rewrite the second exponent as (1+24):

`\implies 4.8* 10^(24)-7.9 * 10^((1+24))`

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

`\implies 4.8* 10^(24)-7.9 * 10^1 * 10^(24)`

Simplify:

`\implies 4.8* 10^(24)-7.9 * 10 * 10^(24)`

`\implies 4.8* 10^(24)-79 * 10^(24)`

Factor out the common term 10²⁴:

`\implies (4.8-79)10^(24)`

Carry out the subtraction inside the parentheses:

`\implies -74.2 * 10^(24)`

To write the answer in scientific notation
`a * 10^n` then 1 ≤ a < 10.

Therefore, divide -74.2 by 10, which means we need to multiply 10²⁴ by 10:

`\implies -74.2 / 10 * 10^(24) * 10`

`\implies -7.42 * 10^(24) * 10^1`

`\implies -7.42 * 10^((24+1))`

`\implies -7.42 * 10^(25)`