Dear Students, Surds and Indices are the bone of algebra. Rules of Surds and Rules of Indices we have given below, you must know these formula to solve the questions based on it smoothly.

**Important Rules of Indices:**
a

^{m}×a^{n}=a^{m+n}^{}

a

^{m}/a^{n}=a^{m-n}^{}

(a

^{m})^{n}=a^{mn}^{}

(ab)

^{n}=a^{n}b^{n}^{}

(a/b)

^{n}=a^{n}/b^{n}^{}

a

^{0}=1**Important Rules of Surds:**

Once you remember the above formula, you will be able to do any complex questions based on it. We are doing some questions with shortcut solutions.

Q1. 102

^{?}×102^{5.6}= 102^{3.4}**Shortcut Solution:**

102

^{?}×102^{5.6}= 102^{3.4}
Or, 102

^{?+5.6}= 102^{3.4}
Or, ?+5.6 = 3.4

Or, ?=3.4-5.6=-2.2

Q2. If (a/b)

^{x-1}=(b/a)^{x-3 }then find the value of x.**Shortcut Solution:**

(a/b)^x-1=(b/a)^x-3

can be written as :

After cross multiplication :

(a)^(2x-4)=(b)^(2x-4)

=>(a/b)^(2x-4)=1

=>(a/b)^(2x-4)=(a/b)^0

=> 2x-4=0

=>x=4/2

=>x=2

Q3. If
10

^{0.48}= x, 10^{0.70}= y and x^{z}= y^{2}, then the value of z is close to:**Shortcut Solution:**

Do this question in three steps:

Step1: zlog(10^0.48)=2log(10^0.70)

Step2: z✕0.48=2✕0.70 (Log10=1)

Step3: z= 2.9

Q4. Given that 5

^{a}= 3125, then the value of 5^{(a - 3)}is:**Shortcut Solution:**

5^(a-3) = 5^a/5^3.

= 3125/125.

= 25

Q5. If
3

^{(x - y)}= 27 and 3^{(x + y)}= 243, then x=?**Shortcut Solution:**

x-y = 3

x+y = 5

________

2x = 8

________

2x/2 = 8/2.

x = 8/2.

so, x = 4.

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