Exponents and scientific notation

Rules

100

(a^m)ⁿ = a^mn 

Power law

200

a⁰ = 1.

Zero law

300

a^m × aⁿ = a^m+n 

Product law

400

a^m/aⁿ = a^m-n 

Quotient law

500

a^-m = 1/a^m

Inverse law

Addition

100

1.11x10³ + 1.11x10²

1.221x10³

200

1.536x10⁸ + 1.524x10⁶

2.55124x10⁸

300

7.49x10⁵ + 6.51x10⁴

8.141x10⁵

400

1.26x10⁴ + 1.12x10³

1.372x10⁴

500

6.88x10⁴ + 2.22x10²

6.9x10⁴

Compare

100

Which is bigger? 45,000 or 4.5x10³

45,000

200

Which is smaller? 9,000,000 or 9x10⁹

9,000,000

300

Which is smaller? 700 or 7.00x10³

700

400

Which is bigger? 89,000 or 8.9x10^-4

89,000 

500

Which one is correct? 6.7x10³ = 67,000 or 5.4x10⁴ = 54,000

5.4x10⁴ = 54,000

Anything Goes

100

Convert into scientific notation: 0.0000345

3.45x10^-5

200

Convert to scientific notation: 0.03452

3.452x10^-2

300

(6.214x10⁸) - (5.71x10⁶)

6.1569x10⁸

400

(2.22x10³) - (1.11x10²)

2.109x10³

500

(1.689x10⁹) - (5.62x10⁶)

1.68338x10⁹

Multiplying

100

(2x10³)(4x10³)

8x10⁶

200

(6x10⁷)(7x10^-3)

4.2x10⁵

300

(120x10^-5)(5x10^-10)

6x10^-13

400

(64x10⁶)(8x10³)

5.12x10¹¹

500

(8x10⁴)(6x10^-8)

4.8x10^-3