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 an = b.

(ii) For n ∈ N, n odd, b ∈ R, there is a unique a ∈ R such that an = b. In both cases a is called the nth root of b or radical and is denoted by b1/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  x2 = a2, has two solutions x = a, x = −a; but a2 = |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

(an)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 (x1/2 + x−1/2)2 = 9/2, then find the value of (x1/2 − x−1/2) for x > 1.        Solution

(4)  Simplify and hence find the value of n: 32n923−n/33n = 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 Solution

(8)  Simplify

If x = √2 + √3 find (x2 + 1)/(x2 − 2)    Solution After having gone through the stuff given above, we hope that the students would have understood "Exponents and Radicals Worksheet for Grade 11".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 