How To Do Exponents By Justin Villaganas

Miscellaneous Powers

100

What is x⁰?

x⁰=1

Final Answer = 1

200

What is (7x)⁰?

(7x)⁰ = 1

Final Answer = 1 

300

What is (6x²z³)^0?

(6x²z³)⁰ = 1

Final Answer = 1

400

What is (7x²3z⁴y³)⁰/(x²3z⁴y³)⁰ ?   

(7x²3z⁴y³)⁰/(x²3z⁴y³)⁰ 

Solution = 1/1 

Final Answer = 1

500

What is (7²x⁴y⁷z⁸)⁰/(6²x³y⁵z⁵)⁰ ?

(7²x⁴y⁷z⁸)⁰/(6²x³y⁵z⁵)⁰

Solution = 1/1

Final Answer = 1

Negative Exponents

100

What is 6^-3 ?

6^-3

Solution = 1/6³

Final Answer = 1/6³

200

What is 7a^-3 ?

7a^-3

Solution = 7/a³

Final Answer = 7/a³

300

What is 6b^-3c⁵ ?

6b^-3c⁵

Solution = 6c⁵/b^-3

Final Answer = 6c⁵/b^-3

400

What is 7b⁴c³d^-5/r^-3 ?

7b⁴c³d^-5/r^-3 

Solution = 7b⁴c³r³/d⁵

Final Answer = 7b⁴c³r³/d⁵

500

What is 7x⁵b³z^-6/y^-5c⁴

7x⁵b³z^-6/y^-5c⁴          

Solution = 7x⁵b³y⁵/z⁶c⁴

Final Answer =7x⁵b³y⁵/z⁶c⁴

Quotient Rule of Powers

100

What is 7b/5b ?

7b/5b

Solution = 2b

Final Answer = 2b

200

What is 6x⁴/x² ?

6x⁴/x²

Solution = x^4-2

Final Answer = 6x²

300

What is 5x⁴c²/xc² ?

5x⁴c²/xc²

Solution = x^4-1 = x³

c^2-2 = 0

Final Answer = 5x³

400

What is 2x⁵z⁵/x⁷b⁵ ?

2x⁷z⁵/x⁵b⁵

Solution = x^7-5 = x²

= 2x²z⁵/b⁵ 

Final Answer = 2z⁵/x²b⁵

500

What is 7x⁷b³z⁶/x⁶bz⁸c³ ?

7x⁷b³z⁶/x⁶bz⁸c³                  

Solution = x^7-6 = x        

b^3-1 = b²

z^8-6 = z²

Final Answer = 7xb²z²/c³

Product Rule of Powers

100

What is 5x² times 4x³ ?

5x² times 4x³

Solution = 9x⁵

Final Answer = 9x⁵

200

What is 7x⁴ times x^-3 ?

7x⁴ times x^-3

Solution = 7x⁴

Final Answer = 7x⁴

300

What is 7xv³ times x³ ?

7xv³ times x³

Solution = x¹⁺³ = x⁴

Final Answer = 7x⁴v³

400

What is 6x³b⁵ times 7x^-3b⁹c³ ?

6x³b⁵ times 7x^-3b⁹c³ 

Solution = x^3+(-3) = 1

 b^{5+9 =} b¹³

Final Answer = 13b¹³c³ 

500

What is 7x³b⁵c⁴ times 67x⁵b⁹c² ?

7x³b⁵c⁴ times 67x⁵b⁹c²

Solution = x³⁺⁵ = x⁸

b⁹⁺⁵ = b¹⁴

c⁴⁺² = c⁶

Final Answer = 74x⁸b¹⁴c⁶

​​​​

Properties of Exponents

100

What is (6x^-3)² ?

(6x^-3)² 

Solution = 6²x^-6

= 36x^-6

Final Answer = 36/x⁶

200

What is (5x³)^-2/(3²)² ? 

(5x³)^-2/(3²)²

Solution = 5^-2x^-6/3⁴

= 3⁴x⁶5²

Final Answer = 106x⁶

300

What is 3x³z⁴c²/12xc³ ?

3x³z⁴c²/12xc3 

Solution = x³z⁴c²/4xc³

= x^3-1

c^2-3

= x²z⁴c^-1/4

Final Answer x²z⁴/4c

400

What is 6q³(z^-3x⁵)^-3/3q² ? 

6q³(z^-3x⁵)^-3/3q²

Solution = 6q³z⁹x^-15/3q²

= 2q³z⁹x^-15/q²

= q^3-2

= 2qz⁹x-¹⁵

Final Answer = 2qz⁹/x¹⁵

500

What is 7x³b⁶z³y⁹/(10x⁴b⁷z⁹yc^-5)^-3 ?

7x³b⁶z³y⁹/(10x⁴b⁷z⁹yc^-5)^-3

Solution = 7x³b⁶z³y⁹/10^-12b^-21z^-27y^-3c¹⁵

= x^3-(-12)= x¹⁵

b^6-(-21) = b²⁷

z^3-(-27) = z³⁰

y^9-(-3) = y¹²

Final Answer = 7x¹⁵b²⁷z³⁰y¹²/c¹⁵