# Selina solutions for Concise Mathematics Class 9 ICSE chapter 7 - Indices (Exponents) [Latest edition]

## Chapter 7: Indices (Exponents)

Exercise 7 (A)Exercise 7 (B)Exercise 7 (C)
Exercise 7 (A) [Page 98]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 7 Indices (Exponents) Exercise 7 (A) [Page 98]

Exercise 7 (A) | Q 1.1 | Page 98

Evaluate :
3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)

Exercise 7 (A) | Q 1.2 | Page 98

Evaluate :
5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)

Exercise 7 (A) | Q 1.3 | Page 98

Evaluate :
( 27/125 )^(2/3) xx ( 9/25 )^(3/2)

Exercise 7 (A) | Q 1.4 | Page 98

Evaluate :
7^0 xx (25)^(-3/2) - 5^(-3)

Exercise 7 (A) | Q 1.5 | Page 98

Evaluate :
(16/81 )^(-3/4) xx (49/9)^(3/2) ÷ (343/216)^(2/3)

Exercise 7 (A) | Q 2.1 | Page 98

Simplify :
( 8x^3 ÷ 125y^3 )^(2/3)

Exercise 7 (A) | Q 2.2 | Page 98

Simplify :
( a + b )^(-1) . ( a^(-1) + b^(-1) )

Exercise 7 (A) | Q 2.3 | Page 98

Simplify :
[ 5^( n + 3 ) - 6 xx 5^( n + 1 )]/[ 9 xx 5^n - 5^n xx 2^2 ]

Exercise 7 (A) | Q 2.4 | Page 98

Simplify :
( 3x^2 )^(-3) xx ( x^9 )^(2/3)

Exercise 7 (A) | Q 3.1 | Page 98

Evaluate :
sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)

Exercise 7 (A) | Q 3.2 | Page 98

Evaluate :
(27/8)^(2/3) - (1/4)^-2 + 5^0

Exercise 7 (A) | Q 4.1 | Page 98

Simplify the following and express with positive index :
(3^-4/2^-8)^(1/4)

Exercise 7 (A) | Q 4.2 | Page 98

Simplify the following and express with positive index :
([27^-3]/[9^-3])^(1/5)

Exercise 7 (A) | Q 4.3 | Page 98

Simplify the following and express with positive index :
(32)^(-2/5) ÷ (125)^(-2/5)

Exercise 7 (A) | Q 4.4 | Page 98

Simplify the following and express with positive index :
[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1

Exercise 7 (A) | Q 5 | Page 98

If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a  x 2-b x 5-c.

Exercise 7 (A) | Q 6 | Page 98

If 1960 = 2a. 5b. 7c, calculate the value of 2-a. 7b. 5-c.

Exercise 7 (A) | Q 7.1 | Page 98

Simplify :
[ 8^3a xx 2^5 xx 2^(2a) ]/[ 4 xx 2^(11a) xx 2^(-2a) ]

Exercise 7 (A) | Q 7.2 | Page 98

Simplify :
[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]

Exercise 7 (A) | Q 8 | Page 98

Show that :
( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1

Exercise 7 (A) | Q 9 | Page 98

If a = xm + n. yl ; b = xn + l. ym and c = xl + m. yn,

Prove that : am - n. bn - l. cl - m = 1

Exercise 7 (A) | Q 10.1 | Page 98

Simplify :
( x^a/x^b)^( a^2 + ab + b^2 ) xx (x^b/x^c)^(b^2 + bc + c^2) xx (x^c/x^a)^( c^2 + ca + a^2 )

Exercise 7 (A) | Q 10.2 | Page 98

Simplify :
( x^a/x^-b )^( a^2 - ab + b^2 ) xx ( x^b/x^-c )^( b^2 - bc + c^2 ) xx ( x^c/x^-a )^( c^2 - ca + a^2 )

Exercise 7 (B) [Pages 100 - 101]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 7 Indices (Exponents) Exercise 7 (B) [Pages 100 - 101]

Exercise 7 (B) | Q 1.1 | Page 100

Solve for x : 22x+1 = 8

Exercise 7 (B) | Q 1.2 | Page 100

Solve for x : 25x-1 = 4 23x + 1

Exercise 7 (B) | Q 1.3 | Page 100

Solve for x :  34x + 1 = (27)x + 1

Exercise 7 (B) | Q 1.4 | Page 100

Solve for x : (49)x + 4 = 72 x (343)x + 1

Exercise 7 (B) | Q 2.1 | Page 100

Find x, if : 42x = 1/32

Exercise 7 (B) | Q 2.2 | Page 100

Find x, if : sqrt( 2^( x + 3 )) = 16

Exercise 7 (B) | Q 2.3 | Page 100

Find x, if : ( sqrt(3/5))^( x + 1) = 125/27

Exercise 7 (B) | Q 2.4 | Page 100

Find x, if : (root(3)( 2/3))^( x - 1 ) = 27/8

Exercise 7 (B) | Q 3.1 | Page 100

Solve :  4x - 2 - 2x + 1 = 0

Exercise 7 (B) | Q 3.2 | Page 100

Solve : [3^x]^2 : 3x = 9 : 1

Exercise 7 (B) | Q 4.1 | Page 100

Solve : 8 x 22x + 4 x 2x + 1 = 1 + 2x

Exercise 7 (B) | Q 4.2 | Page 100

Solve : 22x + 2x+2 - 4 x 23 = 0

Exercise 7 (B) | Q 4.3 | Page 100

Solve : (sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )

Exercise 7 (B) | Q 5 | Page 100

Find the values of m and n if :
4^(2m) = ( root(3)(16))^(-6/n) = (sqrt8)^2

Exercise 7 (B) | Q 6 | Page 100

Solve x and y if : ( √32 )x ÷ 2y + 1 = 1 and 8y - 164 - x/2 = 0

Exercise 7 (B) | Q 7.1 | Page 100

Prove that : ((x^a)/(x^b))^( a + b - c ) (( x^b)/(x^c))^( b + c - a )((x^c)/(x^a))^( c + a - b)

Exercise 7 (B) | Q 7.2 | Page 100

Prove that :
[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1

Exercise 7 (B) | Q 8 | Page 100

If ax = b, by = c and cz = a, prove that : xyz = 1.

Exercise 7 (B) | Q 9 | Page 100

If ax = by = cz and b2 = ac, prove that : y = [2az]/[x + z]

Exercise 7 (B) | Q 10 | Page 101

If 5-P = 4-q = 20r, show that : 1/p + 1/q + 1/r = 0

Exercise 7 (B) | Q 11 | Page 101

If m ≠ n and (m + n)-1 (m-1 + n-1) = mxny, show that : x + y + 2 = 0

Exercise 7 (B) | Q 12 | Page 101

If 5x + 1 = 25x - 2, find the value of  3x - 3 × 23 - x.

Exercise 7 (B) | Q 13 | Page 101

If 4x + 3 = 112 + 8 × 4x, find the value of (18x)3x.

Exercise 7 (B) | Q 14.1 | Page 101

Solve for x :  4x-1 × (0.5)3 - 2x = (1/8)^-x

Exercise 7 (B) | Q 14.2 | Page 101

Solve for x :  (a3x + 5)2. (ax)4 = a8x + 12

Exercise 7 (B) | Q 14.3 | Page 101

Solve for x : (81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27

Exercise 7 (B) | Q 14.4 | Page 101

Solve for x : 23x + 3 = 23x + 1 + 48

Exercise 7 (B) | Q 14.5 | Page 101

Solve for x :  3(2x + 1) - 2x + 2 + 5 = 0

Exercise 7 (B) | Q 14.6 | Page 101

Solve for x : 9x+2 = 720 + 9x

Exercise 7 (C) [Page 101]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 7 Indices (Exponents) Exercise 7 (C) [Page 101]

Exercise 7 (C) | Q 1.1 | Page 101

Evaluate : 9^(5/2) - 3 xx 8^0 - (1/81)^(-1/2)

Exercise 7 (C) | Q 1.2 | Page 101

Evaluate : (64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)

Exercise 7 (C) | Q 1.3 | Page 101

Evaluate : [(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6

Exercise 7 (C) | Q 2 | Page 101

Simplify : [ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]

Exercise 7 (C) | Q 3 | Page 101

Solve : 3x-1× 52y-3 = 225.

Exercise 7 (C) | Q 4 | Page 101

If ((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y , find x + y.

Exercise 7 (C) | Q 5 | Page 101

If 3x + 1 = 9x - 3 , find the value of 21 + x.

Exercise 7 (C) | Q 6 | Page 101

If 2x = 4y = 8z and 1/(2x) + 1/(4y) + 1/(8z) = 4 , find the value of x.

Exercise 7 (C) | Q 7 | Page 101

If [ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3

Show that : m - n = 1.

Exercise 7 (C) | Q 8 | Page 101

Solve for x : (13)√x = 44 - 34 - 6

Exercise 7 (C) | Q 9 | Page 101

If 34x = ( 81 )-1 and 10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y

Exercise 7 (C) | Q 10 | Page 101

Solve : 3(2x + 1) - 2x+2 + 5 = 0.

Exercise 7 (C) | Q 11 | Page 101

If (am)n = am .an, find the value of : m(n - 1) - (n - 1)

Exercise 7 (C) | Q 12 | Page 101

If m = root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]

Exercise 7 (C) | Q 13 | Page 101

Evaluate :
[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]

Exercise 7 (C) | Q 14 | Page 101

Evaluate : ((x^q)/(x^r))^(1/(qr)) xx ((x^r)/(x^p))^(1/(rp)) xx ((x^p)/(x^q))^(1/(pq))

Exercise 7 (C) | Q 15.1 | Page 101

Prove that : a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = 2/(b^2 - a^2 )

Exercise 7 (C) | Q 15.2 | Page 101

Prove that : ( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc

Exercise 7 (C) | Q 16 | Page 101

Evaluate : 4/(216)^(-2/3) + 1/(256)^(-3/4) + 2/(243)^(-1/5)

## Chapter 7: Indices (Exponents)

Exercise 7 (A)Exercise 7 (B)Exercise 7 (C)

## Selina solutions for Concise Mathematics Class 9 ICSE chapter 7 - Indices (Exponents)

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