Selina solutions concise mathematica class 7 icse Solutions for Chapter 5 exponents including laws of exponents

Q1)Find the value of

(i)6^2

(ii)7^3

(iii)4^4

(iv)5^5

(v)8^3

(vi)7^5

Q2)Evaluate:

(i)2^3\times4^2

(ii)2^3\times5^2

(iii)3^3\times5^2

(iv)2^2\times3^3

(v)3^2\times5^2

(vi)5^3\times2^4

(vii)3^2\times4^2

(viii)\left(4\times3\right)^3

(ix)\left(5\times4\right)^2

Q3) Evaluate:

(i)\left(\frac{3}{4}\right)^4

(ii)\left(-\frac{5}{6}\right)^5

(iii)\left(\frac{-3}{-5}\right)^{^3}

Q4) Evaluate:

(i)\left(\frac{2}{3}\right)^{^3}\times\left(\frac{3}{4}\right)^{^2}

(ii)\left(-\frac{3}{4}\right)^{^3}\times\left(\frac{2}{3}\right)^{^4}

(iii)\left(\frac{3}{5}\right)^{^2}\times\left(-\frac{2}{3}\right)^{^3}

Q5) Which is greater:

(i)2^3\ or\ 3^2

(ii)2^5or\ 5^2

(iii)4^3or\ 3^4

(iv)5^4\ or\ 4^5

Q6) Express each of the following in exponential form :

(i) 512

(ii) 1250

(iii) 1458

(iv) 3600

(v) 1350

(vi) 1176

Q7)If a = 2 and b = 3, find the value of:

(i)\left(a+b\right)^2

(ii)\left(b-a\right)^3

(iii)\left(a\times b\right)^a

(iv)\left(a\times b\right)^b

Q8) Express:

(i) 1024 as a power of 2.

(ii) 343 as a power of 7.

(iii) 729 as a power of 3.

Q9) If 27\times32=3^x\times2^y; find the values of x and y.

Q10) If 64\times625=2^a\times5^b; find:

(i) the values of a and b.

(ii) 2^b\times5^a

Q1) Fill in the blanks :

(i)In 5^2=25, base =………. and index=…………

(ii)If index = 3x and base = 2y, the number =………..

Q2)Evaluate :

(i)2^8\div2^3

(ii)2^3\div2^8

(iii)\left(2^6\right)^0

(iv)\left(3^0\right)^6

(v)8^3\times8^{-5}\times8^4

(vi)5^4\times5^3\div5^5

(vii)5^4\div5^3\times5^5

(viii)4^4\div4^3\times4^0

(ix)\left(3^5\times4^7\times5^8\right)^0

Q3) Simplify, giving solutions with positive index:

(i)2b^6.b^3.5b^4

(ii)x^2y^3.\ 6x^5y.\ 9x^3y^4

(iii)\left(-a^5\right)\ \left(a^2\right)

(iv)\left(-y^2\right)\ \left(-y^3\right)

(v)\left(-3\right)^2\ \left(3\right)^2

(vi)\left(-4x\right)\ \left(-5x^2\right)

(vii)\left(5a^2b\right)\ \left(2ab^2\right)\left(a^3b\right)

(viii)x^{2a+7}.\ x^{2a-8}

(ix)3^y.\ 3^2.\ 3^{-4}

(x)2^{4a}\ .\ 3^{3a}.\ 2^{-a}

(xi)4x^2y^2\div9x^3y^3

(xii)\left(10^2\right)^3\left(x^8\right)^{12}

(xiii)\left(a^{10}\right)^{10}\ \left(1^6\right)^{10}

(xiv)\left(n^2\right)^2-\left(-n^2\right)^2

(xv)-\left(3ab\right)^2\ \left(-5a^2bc^4\right)^2

(xvi)\left(-2\right)^2\times\left(0\right)^3\times\left(3\right)^3

(xvii)\left(2a^3\right)^4\left(4a^2\right)^2

(xviii)\left(4x^2y^3\right)^3\div\left(3x^2y^3\right)^3

(xix)\left(\frac{1}{2x}\right)^3\times\left(6x\right)^2

(xx)\left(\frac{1}{4ab^2c}\right)^{^2}\div\left(\frac{3}{2a^2bc^2}\right)^4

(xxi)\frac{\left(5x^7\right)^3.\left(10x^2\right)^2}{\left(2x^6\right)^7}

(xxii)\frac{\left(7p^2q^9r^5\right)^2\left(4pqr\right)^3}{\left(14p^6q^{10}r^4\right)^{^2}}

Q4) Simplify and express the solution in the positive exponent form :

(i)\frac{\left(-3\right)^3\times2^6}{6\times2^3}

(ii)\frac{\left(2^3\right)^5\times5^4}{4^3\times5^2}

(iii)\frac{36\times\left(-6\right)^2\times3^6}{12^3\times3^5}

(iv)-\frac{128}{2187}

(v)\frac{a^{-7}\times b^{-7}\times c^5\times d^4}{a^3\times b^{-5}\times c^{-3}\times d^8}

(vi)\left(a^3b^{-5}\right)^{-2}

Q5)Evaluate :

(i)6^{-2}\div\left(4^{-2}\times3^{-2}\right)

(ii)\left[\left(\frac{5}{6}\right)^{^2}\times\frac{9}{4}\right)\div\left[\left(-\frac{3}{2}\right)^{^2}\times\frac{125}{216}\right]

(iii)5^3\times3^2+\left(17\right)^0\times7^3

(iv)2^5\times15^0+\left(-3\right)^3-\left(\frac{2}{7}\right)^{^{-2}}

(v)\left(2^2\right)^0+2^{-4}\div2^{-6}+\left(\frac{1}{2}\right)^{-3}

(vi)5^n\times25^{n-1}\div\left(5^{n-1}\times25^{n-1}\right)

Q6) If m^2=-2 and n=2; find the values of :

(i)m+r^2-2mn

(ii)m^n+n^m

(iii)6m^{-3}+4n^2

(iv)2n^3-3m