The Rules Of Powers And Roots

Question 1

When multiplying powers…

Answer 1

…you add the powers

E.g. 5^2 x 5^7 = 5^9

Question 2

When dividing the powers…

Answer 2

…you subtract the powers

E.g. 5^4 / 5^2 = 5^2

Question 3

When raising one power to another…

Answer 3

…You multiply them

E.g. (3^2)^4 = 3^2x4 = 3^8

Question 4

Anything to the power of 1….

Answer 4

…is itself

E.g. 8^1 = 8

Question 5

Anything to the power of zero…

Answer 5

…is just 1

E.g. 3^0 = 1

Question 6

1 to any power…

Answer 6

…is still just 1

E.g. 1^z = 1

Question 7

Fractions - Apply the power to…

Answer 7

…both TOP and BOTTOM

E.g. (8/5)^3 = 8^3/5^3

Question 8

When a number has a negative power…

Answer 8

…you turn it up side down

E.g. 7^-2 = 1/7^2

Question 9

Fractional powers:

1) The power of 1/2 means…
2) The power of 1/3 means…
3) The power of 1/4 means…

Answer 9

1) Square root
2) Cube root
3) Fourth root Etc…

E.g. 25^1/2 = SR25 = 5

Question 10

Two stage fractional powers:

With fractional powers like 64^5/6, always…

Answer 10

…split the fraction into root and a power and do them in hat order, root first, then power.

E.g. 64^5/6 = (64)^1x5/6 = (64^1/6)^5 =(2)^5 =32