### Mathematics Class 10 Lab Manual | 21 Lab Activities

Mathematics Lab Manual Class X   lab activities for class 10 with complete observation Tables strictly according to the CBSE syllabus also very useful & helpful for the students and teachers.

# Mathematics Assignment Class VIIIExponents & Redicals

Important extra questions on Exponents and Redicals class VIII strictly according to the DAV board and CBSE Board, necessary for board examinations.

Assignment  chapter - 3

Question 1 :

(i) Evaluate:  (2/7)y = 1

Ans. y = 0

(ii) Evaluate : (0.000064)5/6.
Ans. 0.00032

(iii) Evaluate : 22x-1 = 8x-3.
Ans. x = 8

(iv) Evaluate: (5o + 6o + 7o + 8o)1/2.
Ans. 2
(v) Evaluate: (3o + 4-1) x 22.
Ans. 5
(vi) Simplify :  $\large (27)^{6/5}\div(27)^{1/5}$

Ans. 27

(vii) Evaluate : $\large \left[5^{2}+(8)^{1/3}\right]^{1/3}$
Ans. 3
(viii) Find x if (16)245 = (32)x.
Ans. x = 196

Question 2 :
(i) Simplify :  (-2)k+1 x (-2)3 = (-2)7.

Ans. k = 3

(ii) Find the value of x if :  2(3x – 3x-1) = 324
Ans. x = 5

(iii)  Find the value of x if  x3 = (100)-4 x 100
Ans. 1/100

(iv)  Simplify :   $\frac{a^{-5}\times b^{-4}}{a^{-8}\times b^{+3}}$

Ans. $\frac{a^{3}}{b^{7}}$

(v) Evaluate:  $\left[\left\{(256)^{-1/2}\right\}^{-1/4}\right]^{2}$
Ans. 4

Question 3 :
Evauate:  $\large \left(1^{3}+2^{3}+3^{3}+4^{3}\right)^{-1/2}$
Ans. 1/10

Question 4 :
Evaluate : (6-1 – 8-1)-1 + (2-1 – 3-1)-1.
Ans. 30

Question 5 :
(i)  If 4x +  4x = 32, then find the value of x.
Ans. x = 2
(ii)  If 4x -  4x-1 = 24, then find the value of x.
Ans. x = 5/2
(iii)  Find the value of x if  $(4^{x-1}+4^{x+1})\div(4^{x-1}-4^{x+1})$
Ans. -17/15

Question 6 :
(i)  Find the value of x if 5x + 5x-1 = 750
Ans. x = 4
(ii)  Find the value of x if 5x - 5x-1 = 100
Ans. x = 3
(iii) If 5x-1 + 5x+1 = 130, find the value of x3.
Ans. x = 2,  x3 = 8
(iv) If 6(5x – 5x-1) = 120, then find the value of x
Ans. x = 2
(v) Find the value of x if 5x + 5x+1 = 53 ✕ 30.
Ans. x = 4

(vi)  If  $\large 5^{5x-1}\div 5^{2x}=5^{2}\times 5^{3}$ , then find the the value of x.
Ans. x = 2

Question 7 :
Find the value of p in  $\large 3^{p}+3^{p+1}=4\times 3^{4p-2}$
Ans. P = 2/3

Question 8 :
Evaluate:  $\frac{1}{(216)^{-2/3}}+\frac{1}{(256)^{-3/4}}+\frac{1}{(243)^{-1/5}}$
Ans. 103

Question 9 :
Find the value of x if   $\large \left(2^{-1}+4^{-1}+6^{-1}+8^{-1}\right)^{x}=\frac{625}{576}$
Ans. x = 2
Question 10 :
(i) Evaluate:  $\large \left[7\left(64^{1/3}+27^{1/3}\right)^{3}\right]^{1/4}$
Ans. 7
(ii) Evaluate : $\left[7\left\{(8)^{1/3}+(125)^{1/3}\right\}^{2}\right]^{1/3}$
Ans. 7

Question 11 :
Find the value of the square root of x if

$\large 5^{-1}\times(125)^{11/3}\div(25)^{1/2}=5^{x}$

Ans. $\large \sqrt{x}=3$

Question 12 :
Find the value of :  $\large \left(\frac{1}{4}\right)^{-2}+\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}$

Ans. 29

Question 13 :
If  $\large 140\sqrt{x}+315=1015$ , then find x.
Ans. x = 25
Question 14 :
Find the value of   $\large \left(\frac{64}{125}\right)^{-2/3}+\frac{1}{\left(\frac{256}{625}\right)^{1/4}}+\frac{\sqrt{25}}{\sqrt[3]{64}}$
Ans. 65/16

Question 15 :
Simplify :   $\frac{3^{-5}\times10^{-5}\times5^{3}\times7^{2}}{5^{-7}\times2^{-5}\times3^{-5}\times7^{3}\times5^{2}}$
Ans. 125/7
Question 16 : Simplify :  $\large \frac{x^{7/2}\times\sqrt{y}}{x^{5/2}\times\sqrt{y^{3}}}$
Ans. x/y

Question 17 :
(i) Evaluate : $4\times(81)^{-1/2}\times\left[(81)^{1/2}+(81)^{3/2}\right]$
Ans. 328
(ii) Evaluate: $5\times(64)^{-1/2}\left[(64)^{1/2}+(64)^{3/2}\right]$
Ans. 325
(iii) Evaluate:  $\large 4\times(0.81)^{-1/2}\times\left[(0.064)^{1/3}+(0.0625)^{1/4}\right]$
Ans. 4

Question 18 :

(i) Simplify :  $\large \frac{\sqrt[3]{1372}\times\sqrt[3]{1458}}{\sqrt[3]{27}}$

Ans. 42

(ii) Evaluate:   $\frac{(125)^{-2/3}\times(625)^{5/4}}{\left(\frac{1}{5}\right)^{-3}}$

Ans. 1
Question 19 :
(i)  If $\large \left(\frac{1}{3}\right)^{-5}\times\left(\frac{1}{3}\right)^{7}=\left(\frac{1}{3}\right)^{2x-1}$ then find the value of x
Ans. x = 3/2
(ii)  Evaluate : $\left\{\left(\frac{1}{3}\right)^{-2}-\left(\frac{1}{2}\right)^{-3}\right\}\div\left(\frac{1}{4}\right)^{-2}$
Ans. 1/16

Question 20 :

Evaluate:  $\left(\frac{-7}{8}\right)^{2+x}=\left(\frac{-7}{8}\right)^{3}\left[\left(\frac{-7}{8}\right)^{2/3}\div\left(\frac{-7}{8}\right)^{-1/3}\right]$

Ans. x = 2

Question 21 :
(i) Evaluate :   $\frac{(25)^{3/2}\times(8)^{-4/3}\times(36)^{-1/2}}{(125)^{2/3}\times(27)^{-2/3}}$
Ans. 15/32

(ii) Evaluate:   $\large \frac{(3^{-2})^{2}\times(5^{6})^{1/3}\times(7^{-3})^{2}}{(3^{-2})^{3}\times(25)^{1/2}\times(7^{-2})^{3}}$
Ans. 45
(iii) Evaluate:  $\frac{(64)^{-1/6}\times(216)^{-1/3}\times(81)^{1/4}}{(512)^{-1/3}\times(16)^{1/4}\times(9)^{-1/2}}$
Ans. 9/2
(iv) Evaluate:  $\frac{(81)^{3/4}\times(216)^{-2/3}\times(125)^{1/3}}{(64)^{1/6}\times(243)^{-2/5}\times(343)^{1/3}}$
Ans. 135/56
(v) Evaluate: $\frac{(256)^{-1/4}\times(36)^{-1/2}\times(81)^{1/4}}{(216)^{-1/3}\times(512)^{-1/3}\times(16)^{1/4}}$
Ans. 3

Question 22 : Find the value of x
$\left[\left(\frac{-5}{6}\right)^{2}\right]^{3/8}\div\left(\frac{-5}{6}\right)^{7/6}=\left(\frac{-5}{6}\right)^{7-x}$
Ans. 89 / 12