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

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