Algebra II Negative Exponents

Question 1

Product of Powers

Answer 1

a^(m)a^(n)=a^(m+n)

Question 2

Quotient of Powers

Answer 2

(a^(m))/(a^(n))=a^(m-n)

Question 3

Power of a Power

Answer 3

(a^(m))^(n)=a^(mn)

Question 4

Power of a Product

Answer 4

(ab)^(m)=a^(m)b^(m)

Question 5

What happens with the negative exponent if it is in the numerator?

Answer 5

If the base with the negative exponent is in the numerator, it moves to the denominator

Question 6

What happens with the negative exponent if it is in the denominator?

Answer 6

If the base with the negative exponent is in the denominator, it moves to the numerator

Question 7

How do you simplify an expression?

Answer 7

1. Use properties of exponents
2. Write the expression with positive exponents
3. Evaluate numerical powers

Question 8

How do you know if an expression is simplified?

Answer 8

• No parentheses
• No like bases
• No negative exponents
• No powers of numbers

Question 9

What is the first method used to simplify a power of a quotient?

Answer 9

Simplify within parentheses, then raise the x quotient to the power

Question 10

What is the second method used to simplify a power of a quotient?

Answer 10

Use the power of a quotient property, then divide

Question 11

Which expression is equivalent to 9^(-2)?

a. -81
b. -18
c. 1/81
d. 1/18

Answer 11

c. 1/81

Question 12

What is the quotient of 2^(4)/2^(-4)?

a. 1/256
b. 1/2
c. 1
d. 256

Answer 12

c. 256

Question 13

What is the product of (3y^(-4))(2y^(-4))?

a. 6/y^(8)
b. 1/6y^(8)
c. 6/y^(16)
d. 1/6y^(16)

Answer 13

a. 6/y^(8)

Question 14

Which expression is equivalent to (1/16)^(-4)?

a. (-16)^(4)
b. 16^(4)
c. ^(4)sqrt(1/16)
d. -(1/16)^(-4)

Answer 14

b. 16^(4)

Question 15

Which expression is equivalent to (10x)^(-3)?

a. 10/x^(3)
b. 1000/x^(3)
c. 1/1000x^(3)
d. 1/10x^(3)

Answer 15

c. 1/1000x^(3)

Question 16

Describe how to simplify the expression 3^(-6)/3^(-4)

a. Divide the bases and then add the exponents.
b. Keep the base the same and then add the exponents
c. Multiply the bases and then subtract the exponents
d. Keep the base the same and then subtract the exponents

Answer 16

d. Keep the base the same and then subtract the exponents

Question 17

What is the quotient of 7^(-7)/7^(-2)?

a. 1/343
b. 1/7
c. 7
d. 49

Answer 17

c. 7

Question 18

Anja simplified the expression 10x^(-5)/-5x^(10) to 15/x^(15). What mistake did Anja make?

a. She divided the exponents instead of subtracting them
b. She divided the coefficients instead of subtracting them
c. She subtracted the coefficients instead of dividing them
d. She subtracted the exponents instead of dividing them

Answer 18

c. She subtracted the coefficients instead of dividing them.

Question 19

What is the quotient of -8x^(6)/4x^(-3)?

a. x^(9)/32
b. 4x^(9)
c. -12/x^(2)
d. -2x^(9)

Answer 19

d. -2x^(9)

Question 20

Which expression is equivalent to (3a)^(-2)?

a. 1/9a^(2)
b. 1/3a^(2)
c. 3/a^(2)
d. 9/a^(2)

Answer 20

a. 1/9a^(2)