**1. Laws of Indices:**

i. a

^{m}x a^{n}= a^{m + n}
ii. a

^{m}/ a^{n}= a^{m - n}
iii. (a

^{m})^{n}= a^{mn}
iv. (ab)

^{n}= a^{n}b^{n}
v. (a/b)

^{n}= (a^{n })/(b^{n})**2. Surds:**

Let

*a*be rational number and**n**be a positive integer such that a^{(1/n)}= nth root of a
Then, is
called a surd of order

*n*.**3. Laws of Surds:**

i.

*nth root of a*= a^{(1/n)}
ii.

*nth root of ab*=*nth root of a***nth root of b*

iii.*nth root of (a/b) = (nth root of a)/ (nth root of b)*

iv.*(nth root of a)*

v.^{n}=a*mth root of(nth root of a))*=*mnth root of a*

vi.*(nth root of a)*^{m}= nth root of(a^{m})

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