exponent rules
Product Rule:
b^x * b^y=
b^(x+y)
x^2*x^3=
x^5
sqrt(100)
10
Rewrite using only positive exponents:
x^-3
1/x^3
Solve the following:
sqrt(x)=7
49
Quotient Rule:
b^x/b^y=
b^(x-y)
x^3*x^7=
x^10
The cube root of 27
3
Rewrite using only positive exponents:
x^2/x^6
1/x^4
Solve the following:
sqrt(x)=-7
No solutions, a square root cannot be negative
Power Rule:
(b^x)^y=
b^(xy)
x^4/x^2
x^2
If a square has area 64, what is its side length?
8
Rewrite using only positive exponents:
x^5*x^-8
1/x^3
Solve the following:
sqrt(x+3)=5
22
Negative Rule:
b^-x=
1/b^x
(12x^9)/(6x^4)
2x^5
If a cube has volume 27, what is its edge length?
3
Rewrite using only positive exponents:
(x^2)^-2
1/x^4
Solve the following:
sqrt(x+5)-4=2
31
Zero Rule:
b^0
1
(x^2)^3*x^-7
x^-1=1/x
If a square has area 79, what is its side length?
sqrt(79)
Rewrite using only positive exponents:
(x^3*x^-5)/x^6
1/x^8
Solve the following:
3*sqrt(x-3)=15
28