B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 6 - Indices [Latest edition]

Evaluate:

(5³)⁴ × (5^–2)⁵

Evaluate:

(7^–2)⁴ × (343)²

Evaluate:

(4^–5)² ÷ 8^–6

Evaluate:

`125^((-2)/3) xx 9^(1/2)`

Evaluate:

27ⁿ × 3^{2 – 3n}

Evaluate:

`(8^2/9^-3)^(1/6)`

Simplify:

`(36a^8)^((-1)/2) (125a^15)^(1/3)`

Simplify:

`(32a^-10)^(1/5) (343a^12)^(1/3)`

Simplify:

`(81a^8)^((-3)/4) (8a^15)^(2/3)`

Simplify:

`((49a^-8)/(25b^6))^((-1)/2)`

Simplify:

`(-27a^9)^(2/3)`

Simplify:

`(81a^-2)^((-1)/2) (ab)^-2`

Simplify:

`(a^((-1)/4) * a^(7/8))/(root(6)(a^3))`

Simplify:

`3^(2n - 1) xx 9^(1 - n)` 

Simplify:

`(5^(1/2) xx 5^(7/2))/25^(3/2)`

Simplify:

`(27/125)^(1/3) xx [(3/2)^-2 ÷ (2/5)^3]`

Find the value of `8^(2/3) + root(3)(27^2) - 32^((-3)/5)`

Find the value of `sqrt(9/16) + (0.008)^((-2)/3) - (7/10)^0`

Find the value of `(27/8)^(2/3) - 7^0 + (1/4)^-2`

Find the value of `9^(3/2) - 3(5)^0 - (1/81)^((-1)/2)`

Find the value of `81^(3/4) - (1/32)^((-2)/5) + 8^(1/3) (1/2)^-1 (4)^0`

Find the value of `16^(3/4) + 2(1/2)^-1 - 3^0 + (0.027)^((-2)/3`

Evaluate:

`(sqrt(50) + sqrt(42))^(1/3) (sqrt(50) - sqrt(42))^(1/3)`

Evaluate:

`(sqrt(3) + sqrt(52))^(1/2) (sqrt(52) - sqrt(3))^(1/2)`

Evaluate:

`[27^(2/3) + 81^(1/2) * 8^(1/3)]^((-1)/3)`

Evaluate:

`[343^(1/3) + 8^(2/3) xx 125^(1/3)]^(1/3)`

Simplify and express with a positive index.

`root(4)(81a^12b^-16)`

Simplify and express with a positive index.

`root(5)(32a^5b^10c^-15)`

Simplify and express with a positive index.

`(root(3)(343a^6b^-9))/(root(4)(16b^4))`

Simplify and express with a positive index.

`(3x^-2)^3 (x^9)^(2/3)`

Simplify and express with a positive index.

`((27y^9)/(64x^6))^(2/3)`

Simplify and express with a positive index.

`root(5)(32a^-10) xx 1/a^-3`

Find the value of x in the following:

4²⁰ + 4²⁰ = 2^x

Find the value of x in the following:

2⁵⁰ + 2^x = 2⁵¹

Find the value of x in the following:

3⁴⁰ + 3⁴⁰ + 3^x = 3⁴¹

Simplify:

`(9^(3n) xx 3^(n + 1))/(27^(n + 1) xx 81^n)`

Simplify:

`(8/125)^(1/3)[(4/9)^(-1/2) ÷ (2/5)^2]`

Simplify:

`[(343/27)^(-1/3) [(5/7)^-2 ÷ (3/5)^3]`

Calculate:

`(49^((-3)/2)xx7^-2)/(343^((-4)/3))`

Calculate:

`20^(1/2) xx 5^(1 1/2)`

Calculate:

`3^(14/3) xx 5^((-4)/3) xx 15^((-2)/3)`

Calculate:

`3^(5/3) xx 2^((-1)/3) xx 36^(2/3)`

Calculate:

`8^(2/3)/(root(3)(2 xx 4^-5)`

Calculate:

`25^((-1)/2) xx 125^(2/3) ÷ 625`

Simplify:

`(x^a)^(b - c) (x^b)^(c - a) (x^c)^(a - b)`

Simplify:

`(x^a/x^b)^(a + b) (x^b/x^c)^(b + c) (x^c/x^a)^(c + a)`

Simplify:

`(x^(a + b) * x^(b + c) * x^(c + a))/(x^a * x^b * x^c)^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 )`

Evaluate:

`(25^(n + 1) * 5^n - 125^n)/(5^(3n) * 2^3)`

Evaluate:

`(343^n + 49^n * 7^(n + 2))/((5 * 7^n)^3 - 25 xx 7^(3n))`

Evaluate:

`(2^(n + 2) + 2^n)/(2^(n + 2) - 2^(n + 1))`

Evaluate:

`(7^(n + 2) - 9 xx 7^n)/(7^(n + 1) xx 5)`

Evaluate:

`(4^(n + 4) - 5 xx 4^(n + 2))/(4^(n + 1) xx 11)`

Solve for x:

`(625)^(x - 1) = (0.008)^(3 - x)`

Solve for x:

`81^(x - 2) = 27^(x + 1)`

Solve for x:

`125^(x - 1) = 25^(x + 2) xx (625)^(x - 1)`

Solve for x:

`36^(x + 1) = 6 xx (216)^(x - 1)`

Solve for x:

`16^(2x - 1) = 8^(x + 2)`

Solve for x:

`5^(2x) * 25^3 * 125^2 = (0.04)^-8`

Solve for x:

`sqrt(27^(x + 1)) = 9^(x - 2)`

Solve for x:

`sqrt((3/4)^(1 - 3x)) = 2 10/27`

Solve for x:

`root(3)((25/49)^(x - 1)) = 2 93/125`

Solve for x:

`(a/b)^(1 - 2x) = root(3)(b/a)`

Find the value of x:

`root(3)(4^0 + 3/5) = (5/8)^(1 - 2x)`

Find the value of x:

`sqrt(5^0 + 3/7) = (0.49)^(2 - 3x)`

Find the value of x:

`3^2(7^0 + 4^(3x)) = 9 9/16`

Find the value of x:

`5^2(3^0 + 6^(2x)) = 25 25/36`

The value of 4^–2 is ______.

`(16/625)^(-1/4)` = ______.

`(-27a^9)^(-2/3)` = ______.

`(0.008)^(-2//3)` = ______.

(0.75)^–2 = ______.

2²⁰ + 2²⁰ = ______.

(9^–5)² ÷ (27)^–6 = ______.

`[27^(1//3) + 8^(1//3)]^-3` = ______.

`9^(2x - 1) = 27^(x + 2)`

∴ x = ______.

`sqrt(3) xx root(3)(9) xx root(6)(3^5)` = ______.

`root(4)(16^-2)` = ______.

(81)^0.25 = ______.

8^x = 16 then x = ______.

(0.01)^–0.5 = ______.

`3^(x+4) = 27^x`

∴ x = ______.

2²⁰ + 16⁵ = ______.

`sqrt(49^2 + 49 + 50)` = ______.

`1/2` of 4¹⁶ = ______.

Assertion: 7³ × 7⁴ = 7¹²

Reason: a^m × aⁿ = a^{m + n} where a ≠ 0

Assertion: 9⁸ ÷ 9³ = 9⁵

Reason: (a^m)ⁿ = a^mn

Assertion: `(81/49)^((-3)/2) = (7/9)^3`

Reason: `(a/b)^-m = (b/a)^m`

Assertion: If 10^a × 100^2a = 1000⁵ then a = 3

Reason: (a^m)ⁿ = a^mn

Assertion: 2²⁰ + 2²⁰ = 2²¹

Reason: a^m + aⁿ = a^{m + n}

Assertion: If `x^(2//3) = 4`, then `x = 8`

Reason: `a^(m//n) = root(n)(a^m)`

Simplify:

`root(5)(243a^15b^-20)`

Simplify:

`(0.027a^9b^-6)^((-2)/3)`

Simplify:

`((512a^6)/(729b^-9))^((-2)/3)`

Simplify:

`((x^(2 - 3n) * x^(4 + 3n))/x^3)^2`

Simplify:

`((x^(a + b))^3 * (x^(b + c))^3 * (x^(c + a))^3)/((x^a x ^b x^c)^6`

Simplify:

`((a + 1/b)^x (a - 1/b)^y)/((b + 1/a)^x (b - 1/a)^y)`

Solve for y:

`root(3)(5^0 + 3/4) = (4/7)^(2 - y)`

Solve for y:

`2^3 (5^0 + 3^(2y)) = 8 8/27`

Solve for y:

`sqrt((2/5)^(y - 3)) = 39 1/16`

Simplify:

`(4^(3n) + 4^(2n) * 4^(n + 1))/((4 xx 4^n)^3 - 4 xx 4^(3n))`

Simplify:

`(27a^9)^((-1)/3) (64a^15)^(2/3)`

Simplify:

`(2x^-3)^4 (x^8)^(3/2)`

Simplify:

`(81)^(0.25) xx (81)^(0.5) - (16)^(0.75)`

Evaluate:

`[216^(2/3) + 64^(1/3) * 49^(1/2)]^((-1)/3)`

Evaluate:

`(sqrt(31) + sqrt(56))^(1/2) (sqrt(56) - sqrt(31))^(1/2)`

Evaluate:

`(0.008)^((-2)/3) + (1/4)^-2 - (121)^(1/2)`

Evaluate:

`(25/4)^((-1)/2) - (1/27)^(1/3) + 7^0`

Find the value of x if 9²⁰ + 9²⁰ + 9²⁰ = 3^x

Find the value of x if `5^(x - 1) + 5^x + 5^(x + 1) = 775`

If `(5^a * 125^a + 625^a)/(25^-b * 8^(1/3)) = 125`, show that 4a + 2b = 3.

If a = 10³ × 0.0048 and b = 10^–1 × 75, find the values of `sqrt(ab)` and `sqrt(a/b)`.

Solve for x: `2^(3x + 4) = 2^(3x + 2) + 96`.

Solve for x:

`(9/25)^(1 - 2x) = (125/27)^(x - 2)`

Solve for x:

`(5^(x - 1) xx 25^(x + 2))/(5^x xx 125^(x - 2)) = 625`