Properties of Exponents

Combine Like Terms

100

10x+4x =?

*Same variables, so add together*

14x

200

23b-15b=?

*Same variables, so subtract*

8b

300

-21x²+9x²=?

*Same variables, so add. Negative # is larger, so answer should be negative*

-12x²

400

-52a³b⁴- (-13a³b⁴)=?

*Same variables, so add because a negative - negative= positive. The equation becomes -52a³b⁴ + 13a³b⁴*

-39a³b⁴

500

2x⁶+7y²+4y²-6x⁶=?

*Combine 2x⁶ with -6x⁶ and 7y² with 4y²*

-4x⁶+11y²

Multiplying Exponents

100

t³(t⁶)=?

*Multiply exponents= add them together*

t⁹

200

10x³(3x⁸)=?

*Add exponents and multiply numbers*

30x¹¹

300

-5y⁸(9y⁹) = ?

*Multiply -5 and 9 and add 8 and 9*

-45y¹⁷

400

3^-2(4³) =?

*3^-2 has a negative exponent, so find the reciprocal, 1/3², then multiply it by 4³*

4³/3², then simplify to 64/9

500

7x^-4y²(6x^-2y⁵) =?

*x^-4 and x^-2 are negative exponents so find the reciprocal, making the problem 7y²/x⁴(6y⁵/x²). Multiply straight across*

42y⁷/x⁶

Power to a Power

100

(5⁴)² =?

*When multiplying exponents, the base stays the same*

5⁸

200

(x⁹)⁶=?

*Only multiply exponents together, bases remain the same*

x⁵⁴

300

(-8b³)³ =?

*Multiply coefficient,-8, and exponent,3, to the same power*

-512b⁹

400

(3x⁷y⁵)⁴ =?

*Distribute the 4 to everything in parentheses*

81x²⁸y²⁰

500

(-13cd⁸e¹¹)²

*Distribute 2 to everything in the parentheses, -13 should become positive in the answer because - x - = +*

169c²d¹⁶e²²

Multistep Equations

100

(4x²y³)² + 13x⁴y⁶ =?

*Distribute the 2 to everything in the parentheses to get 16x⁴y⁶. 16x⁴y⁶ and 13x⁴y⁶ are like terms, so add them together.*

29x⁴y⁶

200

(2m⁴n⁹)(8m⁵n) + (3m⁷n⁴)(7m²n⁶) =?

*Multiply both sides first to get 16m⁹n¹⁰ and 21m⁹n¹⁰. They are like terms, so add them together.*

37m⁹n¹⁰

300

(7x³y⁶)³ - (2x³y⁶)³ =?

*Distribute to everything in parentheses to get 343x⁹y¹⁸ and 8x⁹y¹⁸. Like terms so subtract.

335x⁹y¹⁸

400

12(x^-3y^-2)⁴ + 9(x^-6y^-4)² =?

*Distribute to everything within the parentheses to get 12x^-12y^-8 and 9x^-12y^-8. Combine like terms, negative exponents = fraction answer*

21/x¹²y⁸ 

500

(6x^-4y^-2)⁴ - (11x^-8y^-4)² =?

*Distribute to everything within the parentheses to get 1,296 x^-16y^-8 and 121x^-16y^-8. Subtract like terms, negative exponents = fraction answer*

1,175/x¹⁶y⁸

Quotient to a Power

100

Simplify:

-4x⁶y⁷/12x⁴y³

*Divide the numerator and denominator by 4 and simplify the exponents*

-x²y⁴/3

200

(16x⁷/8x⁴)³ =?

*Divide the numerator and the denominator by 8 to get (2x³)³. Distribute it to everything in the parentheses.*

8x⁹

300

(7y¹¹/28y⁸)⁴ =?

*Divide the numerator and the denominator by 7 to get y³/4. Distribute it to the numerator and denominator.*

y¹²/256

400

(63b⁸c¹²/9b⁶c⁴)²

*Divide the numerator and denominator by 9 to get (7b²c⁸)². Distribute 2 to everything.*

49b⁴c¹⁶

500

(3x⁶/5y⁴)^-4 =?

*The negative exponent means that the fraction needs to be the reciprocal, (5y⁴/3x⁶)⁴. Then multiply and distribute*

625y¹⁶/81x²⁴