Simplifying Exponential Expressions (Properties of Exponents)

Addition and Subtraction

100

4x²+5x²

9x²

200

3b² + b² - 8b² 

-4b²

300

3a² + 12b² - 6a² - 9b²+a²

-2a²+3b²

400

^{9x2y3+10x2y4-11x2y3+xyz+5x2y4}

-2x²y³+15x²y⁴+xyz

500

2(3x²y⁴)-9x²y+3(x²y⁴)-xy⁴

9x²y⁴-9x²y-xy⁴

Product of Powers

100

x²(x⁵)

x7

200

5x³y²(2xy³)

10x⁴y⁵

300

(-4k³p⁰)(3k²p⁴)

-12k⁵p⁴

400

(x³y²z)(x³y²z)(x³y²z)

x⁹y⁶z³

500

m³n^{3 .} 4m⁰n²p^{2 .} 2m⁵n¹p⁰(2mnp)

16m⁹n⁷p³

Quotient of Powers

100

x⁶ / x²

x⁴

200

3x⁴ / 6x

x³ / 2

300

(9x⁴y³) / (3x⁹y²)

3y  /  x⁵

400

(3x⁹y⁰z³) / (12x^-1y²z)

(x¹⁰z²) / (4y²)

500

[(45x⁴yz³)(xyz)] / (9x⁶y²z⁶)

5 / (xz²)

Power of a Power

100

(x³)²

x⁶

200

(3x⁴)²

9x⁸

300

(x⁶y²z⁴)¹⁰

x⁶⁰y²⁰z⁴⁰

400

(-7x³y⁴z⁵)² + x

49x⁶y⁸z¹⁰ + x

500

[(5x²y⁵z)^{0 .} 5x⁷y¹²]²

25x¹⁴y²⁴

Grab Bag

100

x³+(2x)³

9x³

200

-2x(x²+4x²)

-10x³

300

5x²(x²)+3x² - x³(x)

4x⁴+3x²

400

[(x⁰y⁵z²)⁰(x³y)] / (xy)

x²

500

3(x³y⁴z²)⁵+3x¹⁵y²⁰z¹⁰+(x³y⁴z²)⁰

6x¹⁵y²⁰z¹⁰+1