Chapters
Chapter 2: Compound Interest (Without using formula)
Chapter 3: Compound Interest (Using Formula)
Chapter 4: Expansions (Including Substitution)
Chapter 5: Factorisation
Chapter 6: Simultaneous (Linear) Equations (Including Problems)
Chapter 7: Indices (Exponents)
Chapter 8: Logarithms
Chapter 9: Triangles [Congruency in Triangles]
Chapter 10: Isosceles Triangles
Chapter 11: Inequalities
Chapter 12: Mid-point and Its Converse [ Including Intercept Theorem]
Chapter 13: Pythagoras Theorem [Proof and Simple Applications with Converse]
Chapter 14: Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter 15: Construction of Polygons (Using ruler and compass only)
Chapter 16: Area Theorems [Proof and Use]
Chapter 17: Circle
Chapter 18: Statistics
Chapter 19: Mean and Median (For Ungrouped Data Only)
Chapter 20: Area and Perimeter of Plane Figures
Chapter 21: Solids [Surface Area and Volume of 3-D Solids]
Chapter 22: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]
Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter 24: Solution of Right Triangles [Simple 2-D Problems Involving One Right-angled Triangle]
Chapter 25: Complementary Angles
Chapter 26: Co-ordinate Geometry
Chapter 27: Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
Chapter 28: Distance Formula

Chapter 7: Indices (Exponents)
Selina solutions for Concise Mathematics Class 9 ICSE Chapter 7 Indices (Exponents) Exercise 7 (A) [Page 98]
Evaluate :
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`
Evaluate :
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`
Evaluate :
`( 27/125 )^(2/3) xx ( 9/25 )^(3/2)`
Evaluate :
`7^0 xx (25)^(-3/2) - 5^(-3)`
Evaluate :
`(16/81 )^(-3/4) xx (49/9)^(3/2) ÷ (343/216)^(2/3)`
Simplify :
`( 8x^3 ÷ 125y^3 )^(2/3)`
Simplify :
`( a + b )^(-1) . ( a^(-1) + b^(-1) )`
Simplify :
`[ 5^( n + 3 ) - 6 xx 5^( n + 1 )]/[ 9 xx 5^n - 5^n xx 2^2 ]`
Simplify :
`( 3x^2 )^(-3) xx ( x^9 )^(2/3)`
Evaluate :
`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`
Evaluate :
`(27/8)^(2/3) - (1/4)^-2 + 5^0`
Simplify the following and express with positive index :
`(3^-4/2^-8)^(1/4)`
Simplify the following and express with positive index :
`([27^-3]/[9^-3])^(1/5)`
Simplify the following and express with positive index :
`(32)^(-2/5) ÷ (125)^(-2/5)`
Simplify the following and express with positive index :
`[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1`
If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a x 2-b x 5-c.
If 1960 = 2a. 5b. 7c, calculate the value of 2-a. 7b. 5-c.
Simplify :
`[ 8^3a xx 2^5 xx 2^(2a) ]/[ 4 xx 2^(11a) xx 2^(-2a) ]`
Simplify :
`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`
Show that :
`( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1`
If a = xm + n. yl ; b = xn + l. ym and c = xl + m. yn,
Prove that : am - n. bn - l. cl - m = 1
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 )`
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 )`
Selina solutions for Concise Mathematics Class 9 ICSE Chapter 7 Indices (Exponents) Exercise 7 (B) [Pages 100 - 101]
Solve for x : 22x+1 = 8
Solve for x : 25x-1 = 4 23x + 1
Solve for x : 34x + 1 = (27)x + 1
Solve for x : (49)x + 4 = 72 x (343)x + 1
Find x, if : 42x = `1/32`
Find x, if : `sqrt( 2^( x + 3 )) = 16`
Find x, if : `( sqrt(3/5))^( x + 1) = 125/27`
Find x, if : `(root(3)( 2/3))^( x - 1 ) = 27/8`
Solve : 4x - 2 - 2x + 1 = 0
Solve : `[3^x]^2` : 3x = 9 : 1
Solve : 8 x 22x + 4 x 2x + 1 = 1 + 2x
Solve : 22x + 2x+2 - 4 x 23 = 0
Solve : `(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`
Find the values of m and n if :
`4^(2m) = ( root(3)(16))^(-6/n) = (sqrt8)^2`
Solve x and y if : ( √32 )x ÷ 2y + 1 = 1 and 8y - 164 - x/2 = 0
Prove that : `((x^a)/(x^b))^( a + b - c ) (( x^b)/(x^c))^( b + c - a )((x^c)/(x^a))^( c + a - b)`
Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`
If ax = b, by = c and cz = a, prove that : xyz = 1.
If ax = by = cz and b2 = ac, prove that : y = `[2az]/[x + z]`
If 5-P = 4-q = 20r, show that : `1/p + 1/q + 1/r = 0`
If m ≠ n and (m + n)-1 (m-1 + n-1) = mxny, show that : x + y + 2 = 0
If 5x + 1 = 25x - 2, find the value of 3x - 3 × 23 - x.
If 4x + 3 = 112 + 8 × 4x, find the value of (18x)3x.
Solve for x : 4x-1 × (0.5)3 - 2x = `(1/8)^-x`
Solve for x : (a3x + 5)2. (ax)4 = a8x + 12
Solve for x : `(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`
Solve for x : 23x + 3 = 23x + 1 + 48
Solve for x : 3(2x + 1) - 2x + 2 + 5 = 0
Solve for x : 9x+2 = 720 + 9x
Selina solutions for Concise Mathematics Class 9 ICSE Chapter 7 Indices (Exponents) Exercise 7 (C) [Page 101]
Evaluate : `9^(5/2) - 3 xx 8^0 - (1/81)^(-1/2)`
Evaluate : `(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`
Evaluate : `[(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6`
Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
Solve : 3x-1× 52y-3 = 225.
If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.
If 3x + 1 = 9x - 3 , find the value of 21 + x.
If 2x = 4y = 8z and `1/(2x) + 1/(4y) + 1/(8z) = 4` , find the value of x.
If `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`
Show that : m - n = 1.
Solve for x : (13)√x = 44 - 34 - 6
If 34x = ( 81 )-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `
Solve : 3(2x + 1) - 2x+2 + 5 = 0.
If (am)n = am .an, find the value of : m(n - 1) - (n - 1)
If m = `root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]`
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)]`
Evaluate : `((x^q)/(x^r))^(1/(qr)) xx ((x^r)/(x^p))^(1/(rp)) xx ((x^p)/(x^q))^(1/(pq))`
Prove that : `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = 2/(b^2 - a^2 )`
Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`
Evaluate : `4/(216)^(-2/3) + 1/(256)^(-3/4) + 2/(243)^(-1/5)`
Chapter 7: Indices (Exponents)

Selina solutions for Concise Mathematics Class 9 ICSE chapter 7 - Indices (Exponents)
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Concepts covered in Concise Mathematics Class 9 ICSE chapter 7 Indices (Exponents) are Handling Positive, Fraction, Negative and Zero Indices, Simplification of Expressions, Solving Exponential Equations, Laws of Exponents.
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