Algebra Club - CHART C - Exponents

Product Rule for Exponents

100

Simplify using Laws of Exponents: 

c · c⁵

c⁶

200

Simplify using Laws of Exponents: 

b¹² * b⁸

b²⁰

300

Simplify using Laws of Exponents: 

d²² · d¹²

d³⁴

400

Simplify using Laws of Exponents: 

(x²⁵x¹³)

x³⁸

500

Simplify using Laws of Exponents: 

(Give answer as a number with no exponent.)

(3²)(3⁵)

2,187

Quotient Rule for Exponents

100

Simplify using Laws of Exponents: 

(3²) / (3¹)

3

200

Simplify using Laws of Exponents: 

(5²³) / (5⁵)

5¹⁸

300

Simplify using Laws of Exponents: 

(x²⁴)/(x³)

x²¹

400

Simplify using Laws of Exponents: 

(Give answer as a number with no exponent.)

(6⁸) / (6⁴)

1,296

500

Simplify using Laws of Exponents: 

[(p⁵)(p¹⁰)] / (p⁵)

p¹⁰

Power Rule for Exponents

100

Simplify using Laws of Exponents:

(w⁴)⁴

w¹⁶

200

Simplify using Laws of Exponents: 

(2x²)³

8x⁶

300

Simplify using Laws of Exponents: 

(b¹²)¹²

b¹⁴⁴

400

Simplify using Laws of Exponents: 

(Simplify to smallest exponent form.)

8¹⁰ / 2⁵

2²⁵

500

Simplify using Laws of Exponents: 

(-9s)(2s³)³

-72s¹⁰

Misc.

100

What operation do we do to the exponents when we have the same bases being multiplied?

Product Rule.

Add the exponents.

200

What operation do we do to the exponents when we have the same bases being divided?

Quotient Rule.

Subtract the exponents.

300

What is the name of this exponent property: 

(x^m)ⁿ = x^mn

Power Rule for Exponents 

400

What is the name of this property?

a^m x aⁿ = a^m+n

Product Rule for Exponents

500

What is the name of this property?

a^m/aⁿ = a^m-n

Quotient Rule for Exponents

Rewrite

100

Rewrite 8 with a base 2 and an exponent.

2³

200

Rewrite 27 with a base 3 and an exponent.

3³

300

Rewrite 32 with a base of 2 and an exponent.

2⁵

400

Evaluate 8^x/2⁵

Simplify to one term with a base of 2.

2^3x-5

500

Evaluate (125^x)(5^y)

Simplify to one term with a base of 5.

5^3x+y

Challenge

100

x^1/3 can be rewritten in radical form. What root of x is taken?

Cubic

200

Evaluate 3^-2

1/9

300

2^4x = 16, what is x?

x = 1

400

If x³ = y⁹, what is x in terms of y?

y³

500

In this equation, what is the value of x-y?

2^x/2^y = 16

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