Standard Index Form

Convert them into ordinary numbers, do the calculation, then change them back if you want the answer in standard form.

For example.

4.5 × 10⁴ + 6.45 × 10⁵

= 45,000 + 645,000

= 690,000

= 6.9 × 10⁵

Here you can use the rules for multiplying and dividing powers. Remember these rules:

• To multiply powers you add, eg, 10⁵× 10³= 10⁸
• To divide powers you subtract, eg, 10⁵÷ 10³= 10²

For Example

Simplify (2 × 10³) × (3 × 10⁶)

How to do it

Multiply 2 by 3 and add the powers of 10:

(2 × 10³) × (3 × 10⁶) = 6 × 10⁹

We can also find zero, negative and fractional powers. The rules below apply to these powers.

PowerAnswerExamples a⁰ 1 4⁰ = 1100⁰ = 137⁰ = 1

Anything to the power 0 is equal to 1.

a^-b

a^1/2

a^1/3

9 to the power of 1/3 = 3