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

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)^(-2/3)`

Simplify the following and express with positive index:

`[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1`

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

If 1960 = 2^a. 5^b. 7^c, calculate the value of 2^-a. 7^b. 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 = x^{m + n}. y^l ; b = x^n + l. y^m and c = x^{l + m}. yⁿ,

Prove that : a^{m - n}. b^n - l. c^{l - 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 )`

Solve for x : 2^2x+1 = 8

Solve for x : 2^5x-1 = 4 2^{3x + 1}

Solve for x:

`3^(4x  +  1) = (27)^(x  +  1)`

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

Find x, if : 4^2x = `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 :  4^{x - 2} - 2^{x + 1} = 0

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

Solve : 8 x 2^2x + 4 x 2^{x + 1} = 1 + 2^x

Solve : 2^2x + 2^x+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 ÷ 2^{y + 1} = 1 and 8^y - 16^{4 - 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 a^x = b, b^y = c and c^z = a, prove that : xyz = 1.

If a^x = b^y = c^z and b² = ac, prove that: y = `[2xz]/[x + z]`

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

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

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

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

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

Solve for x :  (a^{3x + 5})². (a^x)⁴ = a^{8x + 12}

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

Solve for x:

`2^(3x  +  3) = 2^(3x  +  1) + 48`

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

Solve for x : 9^x+2 = 720 + 9^x

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 : 3^x-1× 5^2y-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 3^{x + 1} = 9^{x - 3} , find the value of 2^{1 + x}.

If 2^x = 4^y = 8^z 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 3^4x = ( 81 )^-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `

Solve : 3(2^x + 1) - 2^x+2 + 5 = 0.

If (a^m)ⁿ = a^m .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) = (2b^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)`