**Exponents and Radicals Worksheet for Grade 11 :**

Here we are going to see some practice questions on exponents and radicals.

Before going to see practice questions, let us look into the basic concepts of exponents and radicals.

(i) For n ∈ N, n even, and b > 0, there is a unique a > 0 such that a^{n} = b.

(ii) For n ∈ N, n odd, b ∈ R, there is a unique a ∈ R such that a^{n} = b. In both cases a is called the nth root of b or radical and is denoted by b^{1/n} or ^{n}√b

(i) If n = 2, then nth root is called the square root; if n = 3, then it is called cube root.

(ii) Observe that the equation x^{2} = a^{2}, has two solutions x = a, x = −a; but √a^{2} = |a|.

(iii) Properties of exponents given above are still valid for radicals provided each of the individual terms are defined.

(iv) Note that for n ∈ N and a ≠ 0 we have

(a^{n})^{1/n } = |a| if n is even, a if n is odd

(1) Simplify

(i) (125)^{2/3 }Solution

(ii) (16)^{-3/4 }Solution

(iii) (-1000)^{-2/3 }Solution

(iv) (3^{-6})^{1/3 }Solution

(v) 27^{-2/3}/27^{-1/3 }Solution

(2) Evaluate (((256)^{-1/2})^{-1/4})^{3 }Solution

(3) Evaluate If (x^{1/2} + x^{−1/2})^{2} = 9/2, then find the value of (x^{1/2} − x^{−1/2}) for x > 1. Solution

(4) Simplify and hence find the value of n: 3^{2n}9^{2}3^{−n}/3^{3n} = 27. Solution

(5) Find the radius of the spherical tank whose volume is 32π/3 units. Solution

(6) Simplify by rationalising the denominator.

(7 + √6) / (3 - √2) Solution

(7) Simplify

(8) Simplify

If x = √2 + √3 find (x^{2} + 1)/(x^{2} − 2) Solution

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