RD SHARMA Solutions for Class 9 Maths Chapter 2 - Exponents of Real Numbers
Chapter 2 - Exponents of Real Numbers Exercise Ex. 2.1
Simplify:
3(a4b3)10 × 5(a2b2)3
Simplify:
(2x-2y3)3
Simplify:
Simplify:
Simplify:
Simplify:
If a = 3 and b = -2, find the value of:
aa + bb
If a = 3 and b = -2, find the value of:
ab + ba
If a = 3 and b = -2, find the value of:
(a + b)ab
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Simplify:
Simplify:
Simplify:
Simplify:
Solve the equation for x:
72x + 3 = 1
Solve the equation for x:
2x+1 = 4x-3
Solve the equation for x:
25x + 3 = 8x + 3
Solve the equation for x:
Solve the equation for x:
Solve the equation for x:
23x - 7 = 256
Solve the equation for x:
22x - 2x+3 + 24 = 0
Solve the equation for x:
32x + 4 + 1 = 2.3x + 2
If 49392 = a4b2c3, find the values of a, b and c, where a, b and c are different positive primes.
If 1176 = 2a × 3b × 7c, find a, b and c.
Given 4725 = 3a 5b 7c , find
- the integral values of a, b and c
- the values of 2-a3b7c
If a = xyp - 1, b = xyq-1 and c = xyr-1, prove that aq-rbr-p cp-q = 1.
Chapter 2 - Exponents of Real Numbers Exercise Ex. 2.2
Assuming that x, y, z are positive real numbers, simplify each of the following:
Simplify:
Prove that:
Show that:
Show that:
Show that:
Show that:
Note: Question modified
Note: Question modified
Show that:
(xa-b)a+b(xb-c)b+c(xc-a)c+a = 1
Show that:
Show that:
Show that:
Find the value of x if:
Find the value of x if:
52x + 3 = 1
Find the value of x if:
Find the value of x if:
If x = 21/3 + 22/3, show that x3 - 6x = 6.
Determine (8x)x, if 9x+2 = 240 + 9x.
If 3x+1 = 9x-2, find the value of 21+x.
If 34x = (81)-1 and 101/y = 0.0001, find the value of 2-x+4y.
If 53x = 125 and 10y = 0.001 find x and y.
Solve the equation:
3x + 1 = 27 × 34
Solve the equation:
Solve the equation
3x-1 × 52y-3 = 225
Solve the equation:
Solve the equation:
Solve the equation:
If a and b are different positive primes such that
If a and b are different positive primes such that
(a + b)-1(a-1 + b-1) = axby, find x + y + 2.
If 2x × 3y × 5z = 2160, find x, y and z. Hence, compute the value of 3x × 2-y × 5-z.
If 1176 = 2a × 3b × 7c, find the values of a, b and c. hence, compute the value of 2a × 3b × 7-c as a fraction.
Simplify :
Simplify:
Show that:
If a = xm+nyl, b = xn+lym and c = xl+myn, prove that am-nbn-lcl-m = 1.
If x = am+n, y = an+l and z = al+m, prove that xmynzl = znylzm.
Chapter 2 - Exponents of Real Numbers Exercise 2.29
The value of {2 - 3(2 - 3)3}3 is
(a) 5
(b) 125
(c) 1/5
(d) -125
{2 - 3(2 - 3)3}3
= {2 - 3(-1)3}3
= {2 - 3(-1)}3
= {2 - (-3)}3
= {2 + 3}3
= {5)3
= 53
= 125
So, correct option is (b).
The value of x - yx-y when x = 2 and y = -2 is
(a) 18
(b) -18
(c) 14
(d) -14
x = 2, y = -2
x - y = 2 - (-2) = 2 + 2 = 4
Now x - yx-y = 2 - (-2)4 = 2 - 16 = -14
So, correct option is (d).
The product of the square root of x with the cube root of x is
(a) cube root of the square root of x
(b) sixth root of the fifth power of x
(c) fifth root of the sixth power of x
(d) sixth root of x
Chapter 2 - Exponents of Real Numbers Exercise 2.30
If 8x+1 = 64, what is the value of 32x+1?
(a) 1
(b) 3
(c) 9
(d) 27
8x+1 = 64 = (8)2
so, x + 1 = 2
Hence, x = 1
Now, 32x + 1 = 32(1) + 1 = 33 = 27
Hence, correct option is (d).
If (23)2 = 4x, then 3x =
(a) 3
(b) 6
(c) 9
(d) 27
If x-2 = 64, then x1/3 + x0 =
(a) 2
(b) 3
(c) 3/2
(d) 2/3
Chapter 2 - Exponents of Real Numbers Exercise 2.31
If 9x+2 = 240 + 9x, then x =
(a) 0.5
(b) 0.2
(c) 0.4
(d) 0.1
If x is a positive real number and x2 = 2, then x3 =
Chapter 2 - Exponents of Real Numbers Exercise 2.32
If (16)2x+3 = (64)x+3, then 42x-2 =
(a) 64
(b) 256
(c) 32
(d) 512
Chapter 2 - Exponents of Real Numbers Exercise 2.33
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