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July 8, 2023
On this page you will get to know about, how to solve surds and indices quickly and easy using the formulas and rules.
Indices Multiplication rules:-
23 ⋅ 24 = 2(3+4) = 27 = 2⋅2⋅2⋅2⋅2⋅2⋅2 = 128
Surds Multiplication rules:-
Indices Division rules:-
Surds Division rules:-
Power rule 1
Power rule 2
Power rule 3
Question 1. Find the value of 7-25 – 7-26
Options:
A. 6 × 7-26
B. 6 × 7-25
C. 7 × 7-25
D. 7 × 7-26
Solution: 7-25 – 7-26 = \frac{1}{7^{25}} – \frac{1}{7^{26}}
\frac{7 – 1}{7^{26}} = 6 × 7-26
Correct option: A
Question 2. Simplify (256)^ \frac{3}{4}
A. 16
B. 12
C. 256
D. 64
Solution: (256)^ \frac{3}{4} = (44)^ \frac{3}{4}= 43 = 64
Correct option: D
Question 3. Find the value of 8112 ÷ 8110
A. 72
B. 64
C. 81
D. 49
Solution: We know,
\frac{a^m}{a^n} = am-n
= 8 (112 – 110) = 82 = 64
Correct option: B
Question 1. If 4x + 4x + 1 = 80, then the value of xx is
B. 9
C. 25
D. 4
Solution: 4x(1 + 4) = 80
4x * 5 = 80
4x = \frac{80}{5}
4x = 16
x = 2
xx = 22 = 4
Question 2. If 2a = 3 \sqrt{32}, then a is equal to:
A. \frac{1}{3}
B. 4
C. \frac{5}{3}
D. \frac{1}{2}
Solution: Given value 2a
3 \sqrt{32}
2a = (32)^ \frac{1}{3}
2a = (25)^ \frac{1}{3}
2a = (2)^ \frac{5}{3}
a = \frac{5}{3}
Correct option: C
Question 3. If x and y are whole numbers such that xy = 169, then find the value of (x – 1)y + 1
A. 1331
B. 2744
C. 1728
D. 729
Solution: 169 = 132
So, the value of x = 13 and y = 2
Now, (x – 1)y + 1
= (13 – 1)2+1
= (12)3
=1728
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