Rational Exponents

Product Rule

100

(x⁴)(x⁴)

x⁸

200

(x^-5)(x²)

1 / x¹⁰

300

(5w)(-4w^-4)(2w³)

-40 

400

(24p²q)((1/3)pq)

8p³q²

500

2(2x²y)(-15x⁷y^-3)

-60x⁹ / y²

Quotient Rule

100

(x¹³)/(x⁴)

x⁹

200

25a⁷ / 5a⁵

5a²

300

6x²y³ / 24xy

xy² / 4

400

-15x⁵y³z / -3x⁴y⁷z

5x / y

500

(4ab²)² / (5ab)²

16b² / 25

Fractional Exponents

100

(x^1/2)⁷

x^7/2

200

(3^1/2)(3^3/2)

3² = 9 

300

(16x⁴)^1/2

4x²

400

(4x^1/5) / (24x^5/10) 

1 / 6x^3/10

500

(4³ / 49)^-1/2

7 / 4^3/2

= 7/8

Negative Exponents

100

x^-4

1/x⁴

200

x⁶

1 / x^-6

300

(4p⁵)^-3

1 / 64p¹⁵

400

16w⁴ / 8w^-2

2w⁸

500

(-6x⁴y⁶)² / (2x^-3y⁵)²

9x¹⁴y²

Adding/Subtracting

100

x² + 4x²

5x²

200

2xy² - 6xy²

-4xy²

300

11v² + 4v - 6v² + 8v - v

5v² + 11v

400

17r + 8r - 11r + 6s

14r + 6s 

500

-8a²b³ + 4a²b² - 19a²b³ + 17a²b²

-11a²b³ + 21a²b³