The laws of indices

Question 1

Multiplying indices

Answer 1

when multiplying indices we add the powers.
The base has to be the same.

Question 2

Dividing indices

Answer 2

We subtract the powers. The base must be the same.
20^5/ 5^2 = 3^3

Question 3

Raising a power to a power(a^3)^3

Answer 3

Multiply the two powers together.

Question 4

Power of 0.

Answer 4

Anything to the power of 0 is 1

Question 5

Negative indices

Answer 5

When we have negative indices we make them a fraction, with 1 on the top and the positive indices on the bottom.

Question 6

fractional indices

Answer 6

a^m/n = (^n√a)^m

Question 7

simplify
2x^2(3x+5x) - x(4 - x^2)

Answer 7

6x^2 + 10x^3 - 4x + x^3
11x^3 + 6x^2 - 4x

Question 8

simplify
x^3 - 2x/ 3x^2

Answer 8

(a + b/c can be split into
a/c + b/, a common error is to think that a/b + c = a/b + a/c ) - using this
x^3 - 2x/3x^2 =
x^3/3x^2 - 2x/3x^2 =
x/3 - 2x^-1/3

Question 9

simplify: 2x+x^5/4x^3

Answer 9

= 2x^1/4x^3 + x^5/4x^3
= 1/2x^-2 + 1/4x^2

Question 10

prove that x^1/2 = √x

Answer 10

√x X √x = x
x^1/2 X x^1/2 = x^1
x^1/2 = √x

Question 11

Evaluate 27 ^-1/3

Answer 11

27^-1/3 = (27^1/3)^-1
= 3^-1
=1/3

Question 12

if b = 1/2a^2, determine 3b^-2 in the form ka^n where k,n are constants.

Answer 12

b = 1/2a^2
3b^-2 = 3(1/9a^2)^-2
= 3(81a^-4) = 243a^-4
k = 243
n = - 4