Question

(5 * 10^-2) (4 * 10^-3), write in scientific notation.

Answer 1

`\large \bf \implies{2 * {10}^( - 4) }`

Step-by-step explanation :

`\bf(5 * {10}^( - 2) )(4 * {10}^( - 3) )`

Step 1) : Rewrite the expression

`\bf \longrightarrow(5 * 4) *( {10}^( - 2) * {10}^( - 3) )`

Step 2) : Calculate the product or quotient

`\bf \longrightarrow20 * ( {10}^( - 2) * {10}^( - 3) )`

Step 3) : Simplify using exponent rule with same base

`\bf {a}^(n) . \: {a}^(m) = {a}^(n + m)`

`\bf \longrightarrow20 * {10}^( - 2 - 3)`

Step 4) : Calculate the sum or difference

`\bf \longrightarrow20 * {10}^( - 5)`

Step 5) : Express the number in scientific notation

`\bf \longrightarrow2 * {10}^( - 4)`

Answer 2

`2 * 10^(-4)`

Explanation:

`5 * 10^(-2) * 4 * 10^(-3) \\\to 20 * 10^(-2 + -3) \\\to 2 * 10 * 10^(-5) \\\to 2 * 10^(1 + -5) \\\to 2 * 10^(-4)`