3 Common Errors (Indices)

Iffah (05) & Danish (15)

3 Common Errors & How to Avoid Them

1. Splitting up integers to their base+index.

For example, 4^x = 32.
We need to first split up 4 and 32 to their base form, that is 2^2 and 2^5, for 4 and 32 respectively.

Hence, (2)^2x = 2^5
2x = 5
x = 2.5

You can try looking at common bases that both numbers have.

2. Negative indices.

a ^ (-n) = 1 / a^n

Don't get confused! :) Know that for every negative index, you move it either UP or DOWN of the fraction. Like.....

-(3 ^2) x 3 ^(-3)
= -9 [THE SQUARE BELONGS ONLY TO 9, AND NOT TO -9] x 1 / 3^3
= -9 x 1/27
= -9/27
= -1/3
= - (1/3)

You can make sure you follow the BODMAS law first.

3. Multiplication law. a^b x a^c = a ^(b+c)

For example,

3 ^(1/2) x 3 ^(1/2)
= 3 ^ (1/2 + 1/2)
= 3 ^ 1
= 3.

In this case, it is not 1/2 x 1/2, but instead 1/2 + 1/2! Multiplication law (same base!)

BE DETAILED & GOOD LUCK!

PS. Danish didn't do anything omfg