Properties
What does the negative exponent property do?
a^-x
It makes you take the reciprocal of the base and the exponent becomes positive
1/a^x
Joseph thinks that he solved the following question correctly. Did he? If not, solve it correctly and explain where he went wrong.
(x^4)^2=x^6
No, he added the exponents instead of multiplying them.
(x^4)^2=x^8
((7x^3y^7z^8)/(2x^3y^12z^2))^0
1
(32x^7y^5)/(4x^4y^2)
8x^3y^3
a^-4
1/a^4
What do you do for the power of a power property?
(x^4)^2
You multiply the two exponents together
x^8
Maddie is struggling to explain why the following equation equals 1. How should she explain it?
x^0=1
The zero power property states that anything with an exponent of 0 equals 1, regardless of the base number.
x^2*x^9
x^11
(10x^9)/(5x^7)
2x^2
(ab)^3
a^3b^3
What do you do for the power of a product rule?
(ab)^x
The exponent gets distributed to each base
a^x*b^x
Is the following equation true? If yes, why? If no, why?
(2x^3)^0=2x^3
No, the zero power property makes the answer 1.
a^7/a^5
a^2
(a^2b^2)^0
1
Simplify this completely
x^2/x^5
1/x^3
What do you do when you are multiplying exponents with the same base? (x^7*x^12 )
You keep the base and add the exponents
(x^19)
Is the following equation true? If yes, explain why. If not, explain why.
(4a^4b^7)^2=16a^8b^14
Yes, this is true because when you have a power of a power equation, you multiply the exponents.
n^3*n^7
n^10
(xyz)^3
x^3y^3z^3
x^2*x^7
x^9
What does the zero power property state?
a^0
The answer will be 1 no matter what!!
Is the following equation correct? If not, why? If so, why?
z^-9=1/9z
No, the negative exponent property tells us to take the reciprocal and make the exponent positive.
z^-9=1/z^9
Simplify this completely
(2x^4)/(2x^8)
1/x^4
(x^3)^7
x^21
b^-9
1/b^9