## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Ex 4.1

Question 1.

Fill in the blanks:

(i) In the expression 3^{7}, base = …….. and exponent = ……..

(ii) In the expression (-7)^{5}, base = ………. and exponent = …….

(iii) In the expression \(\left( \frac { 2 }{ 5 } \right) ^{ 11 }\), base = …… and exponent = …….

(iv) If base is 6 and exponent is 8, then exponential form = ……..

Solution:

Question 2.

Find the value of the following:

(i) 2^{6}

(ii) 5^{5}

(v) (-6)^{4}

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

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

(vi) (-2)^{9}

Solution:

Question 3.

Express the following in the exponential form:

(i) 6 × 6 × 6 × 6 × 6

(ii) t × t × t

(iii) 2 × 2 × a × a × a × a

(iv) a × a × a × c × c × c × c × d

Solution:

Question 4.

Simplify the following:

(i) 7 × 10^{3}

(ii) ^{25} × 9

(iii) 3^{3} × 10^{4}

Solution:

Question 5.

Simplify the following:

(i) (-3) × (-2)^{3}

(ii) (-3)^{2} × (-5)^{2}

(iii) (-2)^{3} × (-10)^{4}

(iv) (-1)^{9}

(v) 25^{2} × (-1)^{31}

(vi) 4^{2} × 3^{3} × (-1)^{122}

Solution:

Question 6.

Identify the greater number in each of the following:

(i) 4^{3} or 3^{4}

(ii) 7^{3} or 3^{7}

(iii) 4^{5} or 5^{4}

(iv) 2^{10} or 10^{2}

Solution:

Question 7.

Write the following numbers as powers of 2:

(i) 8

(ii) 128

(iii) 1024

Solution:

Question 8.

To what power (-2) should be raised to get 16?

Solution:

Question 9.

Write the following numbers as powers of (-3):

(i) 9

(ii) -27

(iii) 81

Solution:

Question 10.

Find the value of x in each of the following:

(i) 7^{x} = 343

(ii) 3^{x} = 729

(in) (-8)^{x} = -512

(iv) (-4)^{x} = -1024

(v) \(\left( \frac { 2 }{ 5 } \right) ^{ x }\) = \(\frac { 32 }{ 3125 }\)

(vi) \(\left( \frac { -3 }{ 4 } \right) ^{ x }\) = \(\frac { -243 }{ 1024 }\)

Solution:

Question 11.

Write the prime factorization of the following numbers in the exponential form:

(i) 72

(ii) 360

(iii) 405

(iv) 540

(v) 2280

(vi) 3600

(vii) 4725

(viii) 8400

Solution: