Algebra II Negative Exponents Flashcards
Product of Powers
a^(m)a^(n)=a^(m+n)
Quotient of Powers
(a^(m))/(a^(n))=a^(m-n)
Power of a Power
(a^(m))^(n)=a^(mn)
Power of a Product
(ab)^(m)=a^(m)b^(m)
What happens with the negative exponent if it is in the numerator?
If the base with the negative exponent is in the numerator, it moves to the denominator
What happens with the negative exponent if it is in the denominator?
If the base with the negative exponent is in the denominator, it moves to the numerator
How do you simplify an expression?
- Use properties of exponents
- Write the expression with positive exponents
- Evaluate numerical powers
How do you know if an expression is simplified?
- No parentheses
- No like bases
- No negative exponents
- No powers of numbers
What is the first method used to simplify a power of a quotient?
Simplify within parentheses, then raise the x quotient to the power
What is the second method used to simplify a power of a quotient?
Use the power of a quotient property, then divide
Which expression is equivalent to 9^(-2)?
a. -81
b. -18
c. 1/81
d. 1/18
c. 1/81
What is the quotient of 2^(4)/2^(-4)?
a. 1/256
b. 1/2
c. 1
d. 256
c. 256
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)
a. 6/y^(8)
Which expression is equivalent to (1/16)^(-4)?
a. (-16)^(4)
b. 16^(4)
c. ^(4)sqrt(1/16)
d. -(1/16)^(-4)
b. 16^(4)
Which expression is equivalent to (10x)^(-3)?
a. 10/x^(3)
b. 1000/x^(3)
c. 1/1000x^(3)
d. 1/10x^(3)
c. 1/1000x^(3)
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
d. Keep the base the same and then subtract the exponents
What is the quotient of 7^(-7)/7^(-2)?
a. 1/343
b. 1/7
c. 7
d. 49
c. 7
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
c. She subtracted the coefficients instead of dividing them.
What is the quotient of -8x^(6)/4x^(-3)?
a. x^(9)/32
b. 4x^(9)
c. -12/x^(2)
d. -2x^(9)
d. -2x^(9)
Which expression is equivalent to (3a)^(-2)?
a. 1/9a^(2)
b. 1/3a^(2)
c. 3/a^(2)
d. 9/a^(2)
a. 1/9a^(2)
