## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) In the expression (-5)^{9}, exponent = ……… and base = ………..

(ii) If the base is \(\frac { -3 }{ 4 }\) and exponent is 5, then exponential form is ………

(iii) The expression (x^{2}y^{5})^{3} in the simplest form is ………

(iv) If (100)^{0} = 10^{n}, then the value of n is ……..

(ix) 35070000 = 3.507 × 10^{….}

(x) If (-2)^{n} = -128, then n = ……..

Solution:

(i) In the expression (-5)^{9}, exponent = 9 and base = -5.

(ii) If the base is \(\frac { -3 }{ 4 }\) and exponent is 5, then exponential form is \(\left( -\frac { 3 }{ 4 } \right) ^{ 5 }\)

(iii) The expression (x^{2}y^{5})^{3} in the simplest form is (x^{2})^{3} × (y^{5})^{3} = x^{6}y^{15}.

(iv) If (100)^{0} = 10^{n}, then the value of n is 0.

{∵ (10^{2})^{0} = 10^{n} ⇒ 10^{0} = 10^{n}}

∴ n = 0

Question 2.

State whether the folloiwng statements are true (T) or false (F):

(i) If a is a rational number then a^{m} × a^{n} = a^{m×n}

(ii) 2^{3} × 3^{2} = 6^{5}.

(iii) The value of (-2)^{-3} is \(\frac { -1 }{ 8 }\).

(iv) The value of the expression 2^{9} × 2^{91} – 2^{19} × 2^{81} is 1.

(v) 3^{0} = (1000)^{0}.

(vi) 5^{6} ÷ (-2)^{6} = \(\frac { -5 }{ 2 }\)

(vii) 5^{0} × 3^{0} = 8^{0}

(viii) \(\frac { { 2 }^{ 3 } }{ 7 } <\left( \frac { 2 }{ 7 } \right) ^{ 3 }\)

(ix) (10 + 10)^{4} = 10^{4} + 10^{4}.

(x) x^{0} × x^{0} = x^{0} ÷ x^{0}, where x is a non-zero rational number.

(xi) 4^{9} is greater than 16^{3}.

(xii) x^{m} + x^{m} = x^{2m}, where x is a non-zero rational number and m is a positive integer.

(xiii) \(\left( \frac { 4 }{ 3 } \right) ^{ 5 }\times \left( \frac { 5 }{ 7 } \right) ^{ 5 }=\left( \frac { 4 }{ 3 } +\frac { 5 }{ 7 } \right) ^{ 5 }\)

Solution:

**Multiple Choice Questions**

Choose the correct answer from the given four options (3 to 18):

Question 3.

a × a × a × b × b × b is equal to

(a) a^{3}b^{2}

(b) a^{2}b^{3}

(c) (ab)^{3}

(d) a^{6}b6

Solution:

a × a × a × b × b × b = a^{3}b^{3} = (ab)^{3} (c)

Question 4.

(-2)^{3} × (-3)^{2} is equal to

(a) 6^{5}

(b) (-6)^{6}

(c) 72

(d) -72

Solution:

(-2)^{3} × (-3)^{2} = -8 × 9 = -72

Question 5.

The expression (pqr)^{3} is equal to

(a) p^{3}qr

(b) pq^{3}r

(c) pqr^{3}

(d) p^{3}q^{3}r^{3}

Solution:

(pqr)^{3} = p^{3}q^{3}r^{3} (d)

Question 6.

Solution:

Question 7.

Solution:

Question 8.

The value of (5^{30} × 5^{20}) ÷ (5^{5})^{9} in the exponential form is

(a) 5^{-5}

(b) 5^{5}

(c) 5^{50}

(d) 5^{95}

Solution:

(5^{30} × 5^{20}) ÷ (5^{5})^{9}

= 5^{30+20} ÷ 5^{5×9}

= ^{250} ÷ 5^{45}

= 5^{50-45}

= 5^{5} (b)

Question 9.

The law \(\left( \frac { a }{ b } \right) ^{ n }=\frac { { a }^{ n } }{ b^{ n } }\) does not hold when

(a) a = 3, b = 2

(b) a = -2, b = 3

(c) n = 0

(d) b = 0

Solution:

Question 10

Solution:

Question 11.

Solution:

Question 12.

The value of 5^{-1} – 6^{-1} is

(a) \(\frac { 1 }{ 30 }\)

(b) \(\frac { -1 }{ 30 }\)

(c) 30

(d) -30

Solution:

Question 13.

The value of (6^{-1} – 8^{-1})^{-1} is

(a) \(\frac { -1 }{ 2 }\)

(b) -2

(c) \(\frac { 1 }{ 24 }\)

(d) 24

Solution:

Question 14.

Solution:

Question 15.

If 2^{3} + 1^{3} = 3^{x}, then the value of x is

(a) 0

(b) 1

(c) 2

(d) 3

Solution:

2^{3} + 1^{3} = 3^{x}

⇒ 8 + 1 = 3^{x}

⇒ 9 = 3x

⇒ 3^{2} = 3^{x}

⇒ x = 2 (c)

Question 16.

The standard form of 751.65 is

(a) 7.5165 × 10^{2}

(b) 75.165 × 10^{1}

(c) 7.5165 × 10^{4}

(d) 7.51 × 10^{2}

Solution:

Standard form of 751.65 = 7.5165 × 10^{2} (a)

Question 17.

The usual form of 5.658 × 10^{5} is

(a) 5658

(b) 56580

(c) 565800

(d) 5658000

Solution:

5.658 × 10^{5} = 565800 (c)

Question 18.

Which of the following numbers is in the standard form?

(a) 26.57 × 10^{4}

(b) 2.657 × 10^{4}

(c) 265.7 × 10^{3}

(d) 0.2657 × 10^{6}

Solution:

2.657 × 10^{5} is in standard form. (b)

**Value Based Questions**

Question 1.

Typhoid is caused by bacteria Salmonella typhi. The size of Salmonella typhi is about 0.0000000005 mm. Express it in standard form. Vinay is suffering from typhoid, his doctor advised him to take healthy food and avoid eating food or drinking beverages from street vendors.

Why should we eat healthy food and why should we not eat food from street vendors?

Solution:

Size of Salmonella typhi = 0.0000000005 mm

Standard form = 5.0 × 10^{-10}

We should take healthy food for our healthy body we should not eat or drink from street vendors as it may be unhygienic.

**Higher Order Thinking Skills (HOTS)**

Question 1.

Solution:

Question 2.

Solution: