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As per rule of indices ,There are a number of important rules of index numbers:
ya × yb = ya+b
Examples
24 × 28 = 212
54 × 5-2 = 52
ya ÷ yb= ya-b
Examples
39 ÷ 34 = 35
72 ÷ 75 = 7-3
y -b = 1/yb
Examples
2-3 = 1/23 = 1/8
3-1 = 1/3
ym/n = (n√y)m
Examples
161/2 = √16 = 4
82/3 = (3√8)2 = 4
(yn)m = ynm
Example
25 + 84
= 25 + (23)4
= 25 + 212
y0 = 1
Example
50 = 1
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Let m = loga x and n = loga y
Step 2: Write in exponent form
x = am and y = an
Step 3: Multiply x and y
x • y = am • an = am+n
Step 4: Take log a of both sides and evaluate
log a xy = log a am+n
log a xy = (m + n) log a a
log a xy = m + n
log a xy = loga x + loga y
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