Index laws

Question 1

a^mx aⁿ

Answer 1

a^{m + n}

Question 2

a^m/ aⁿ

Answer 2

a^{m - n}

Question 3

(a^m)ⁿ

Answer 3

a^mn

Question 4

(ab)ⁿ

Answer 4

aⁿbⁿ

Question 5

(a/b)ⁿ

Answer 5

aⁿ/bⁿ

Question 6

a⁰

Answer 6

1

Question 7

a^-m

Answer 7

1/a^m

Question 8

a^m/n

Answer 8

ⁿ√a^m

(nth root of a^m)

Question 9

List the 8 index laws

Answer 9

Question 10

When can you flip a fraction to remove negative exponents?

Answer 10

Only when there are no other operators.

e.g.

(3/x)^-2= (x/3)²

e.g.2

(15m³n^-2/25^-mn^-4) ^-3

^{in this case you flip and either change the sign on the outside exponent OR the signs on the inside.}

>> (25^mn⁴/15^-3n^-2)³

^OR

(25^-mn^-4/15³n²)^-3