Mathematics Assignment Class VIII
Exponents & 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 : 2^2x-1 = 8^x-3.

Ans. x = 8

(iv) Evaluate: (5^o + 6^o + 7^o + 8^o)^1/2.

Ans. 2

(v) Evaluate: (3^o + 4^-1) x 2².

Ans. 5

(vi) Simplify : $(27)^{6/5}\div(27)^{1/5}$

Ans. 27

(vii) Evaluate : $\left[5^{2}+(8)^{1/3}\right]^{1/3}$

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(3^x – 3^x-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: $\left(1^{3}+2^{3}+3^{3}+4^{3}\right)^{-1/2}$

Ans. 1/10

Question 4 :

Evaluate : (6^-1 – 8^-1)^-1 + (2^-1 – 3^-1)^-1.

Ans. 30

Question 5 :

(i) If 4^x + 4^x = 32, then find the value of x.

Ans. x = 2

(ii) If 4^x - 4^x-1 = 24, then find the value of x.

Ans. x = 5/2

(iii) Find the value of $(4^{x-1}+4^{x+1})\div(4^{x-1}-4^{x+1})$

Ans. -17/15

Question 6 :

(i) Find the value of x if 5^x + 5^x-1 = 750

Ans. x = 4

(ii) Find the value of x if 5^x - 5^x-1 = 100

Ans. x = 3

(iii) If 5^x-1 + 5^x+1 = 130, find the value of x³.

Ans. x = 2, x³ = 8

(iv) If 6(5^x – 5^x-1) = 120, then find the value of x
Ans. x = 2
(v) Find the value of x if 5^x + 5^x+1 = 5³ ✕ 30.
Ans. x = 4

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

Ans. x = 2

Question 7 :

Find the value of p in $3^{p}+3^{p+1}=4\times 3^{4p-2}$

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 $\left(2^{-1}+4^{-1}+6^{-1}+8^{-1}\right)^{x}=\frac{625}{576}$

Ans. x = 2

Question 10 :

(i) Evaluate: $\left[7\left(64^{1/3}+27^{1/3}\right)^{3}\right]^{1/4}$
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

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

Ans. $\sqrt{x}=3$

Question 12 :

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

Ans. 29

Question 13 :

If $140\sqrt{x}+315=1015$ , then find x.

Ans. x = 25

Question 14 :

Find the value of $\left(\frac{64}{125}\right)^{-2/3}+\frac{1}{\left(\frac{256}{625}\right)^{1/4}}+\frac{\sqrt{25}}{\sqrt[3]{64}}$

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 : $\frac{x^{7/2}\times\sqrt{y}}{x^{5/2}\times\sqrt{y^{3}}}$

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: $4\times(0.81)^{-1/2}\times\left[(0.064)^{1/3}+(0.0625)^{1/4}\right]$

Ans. 4

Question 18 :

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

Ans. 42

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

Ans. 1

Question 19 :

(i) If $\left(\frac{1}{3}\right)^{-5}\times\left(\frac{1}{3}\right)^{7}=\left(\frac{1}{3}\right)^{2x-1}$ 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: $\frac{(3^{-2})^{2}\times(5^{6})^{1/3}\times(7^{-3})^{2}}{(3^{-2})^{3}\times(25)^{1/2}\times(7^{-2})^{3}}$

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

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Mathematics Assignment Class VIII
Exponents & Redicals