Question

PLSS HELP.
Simplify the expression. Write the answer using scientific notation (7x10^5)^2

Answer 1

`\sf 4.9 * 10^(11)`

Explanation:

Given expression:
`\sf (7 * 10^5)^2`

Apply exponent rule
`\sf (ab)^2=a^2 \cdot b^2` :

`\sf \implies 7^2 * (10^5)^2`

`\sf \implies 49 * (10^5)^2`

Apply exponent rule
`\sf (a^b)^c=a^(bc)` :

`\sf \implies 49 * 10^(5 \cdot 2)`

`\sf \implies 49 * 10^(10)`

Scientific notation:
`\sf a * 10^n`

where
`\sf 1\leq a < 10` and n is an integer

We can write 49 as
`\sf 4.9 * 10=4.9 * 10^1`

`\sf \implies 4.9 * 10^1* 10^(10)`

Apply exponent rule
`\sf a^ba^c=a^(b+c)`

`\sf \implies 4.9 * 10^(11)`