BLANKS [1 Marks Each]

Question 11 Mark

3² _____ 1⁵

Answer

3² < 1⁵
Solution:
$\because$ 3² = 3 × 3 = 9
So, 9 < 15
$\therefore$ 3² < 15

View full question & answer→

Question 21 Mark

a⁶ × a⁵ × a⁰ = a _____.

Answer

a⁶ × a⁵ × a⁰ = a¹¹
Solution:
Since, a⁶ × a⁵ × a⁰
= a⁶⁺⁵⁺⁰
= a¹¹
$\therefore$ a⁶ × a⁵ × a⁰
= a¹¹

View full question & answer→

Question 31 Mark

88880000000 = _____ × 10¹⁰

Answer

88880000000 = 8.888 × 10¹⁰
Solution:
Given, 88880000000
For standard form, 88880000000
= 8888 × 10⁷ Also, 8888
= 8.888 × 10³
So, 8.888 × 10³ × 10⁷
= 8.888 × 10¹⁰
88880000000 = 8.888 × 10¹⁰

View full question & answer→

Question 41 Mark

7⁴ _____ 5⁴

Answer

7⁴>5⁴
Solution:
Obviously, 7⁴>5⁴
[$\because$ powers are same, so if base is greater then the number is greater]

View full question & answer→

Question 51 Mark

729 = 3_____.

Answer

729 = 3⁶

Solution:

Here, firstly we find out the factors of given expression.

$\begin{array}{c|c} 3 & 729 \\ \hline 3 & 243 \\ \hline 3& 81\\ \hline 3 & 27 \\ \hline 3 & 9 \\ \hline 3 & 3 \\ \hline &1 \end{array}$

So, 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶

$\therefore$ 729 = 3⁶

View full question & answer→

Question 61 Mark

6³ _____ 4⁴

Answer

6³ < 4⁴
$\because$ 6³ = 6 × 6 × 6 = 216
and 4⁴ = 4 × 4 × 4 × 4 = 256
So, 216 < 256
$\therefore$ 6³ < 4⁴

View full question & answer→

Question 71 Mark

53700000 = _____ × 10⁷

Answer

53700000 = 5.37 × 10⁷
Solution:
Given, 53700000
For standard form, 53700000
= 537 × 10⁵ Also, 537
= 5.37 × 10²
So, 5.37 × 10² × 10⁵
= 5.37 × 10⁷
53700000 = 5.37 × 10⁷

View full question & answer→

Question 81 Mark

53700000 = _____ × 10⁷

Answer

53700000 = 5.37 × 10⁷
Solution:
Given, 53700000
For standard form, 53700000
= 537 × 10⁵ Also, 537
= 5.37 × 10²
So, 5.37 × 10² × 10⁵
= 5.37 × 10⁷
53700000 = 5.37 × 10⁷

View full question & answer→

Question 91 Mark

432 = 2⁴ × 3 _____.

Answer

432 = 2⁴ × 3³
Solution:
$\begin{array}{c|c} 4 & 432 \\ \hline 2 & 216 \\ \hline 2 & 108 \\ \hline 2 & 54 \\ \hline 3 & 27 \\ \hline 3 & 9 \\ \hline & 1 \end{array}$
Firstly, we find out the factors of given expression.
So, 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3
= 2⁴ × 3³
$\therefore$ 432 = 2⁴ × 3³

View full question & answer→

Question 101 Mark

(-3)⁸ ÷ (-3)⁵ = (-3)____.

Answer

(-3)⁸ ÷ (-3)⁵ = (-3)³
Solution:
Here, (-3)⁸ ÷ (-3)⁵ = (-3)^8-5 = (-3)³[$\because$ a^m + aⁿ = a^m-n, m > n]
^$\therefore$ (-3)⁸ ÷ (-3)⁵ = (-3)³

View full question & answer→

Question 111 Mark

340900000 = 3.409 × 10 _____.

Answer

340900000 = 3.409 × 10⁸
Solution:
For standard form, 340900000 = 3409 × 10⁵
Also, 3409 = 3.409 × 10³
So, 3.409 × 10³ × 10⁵
= 3.409 × 10⁸ [$\therefore$ a^m × aⁿ = a^m+n]
340900000 = 3.409 × 10⁸

View full question & answer→

Question 121 Mark

2³ _____ 3²

Answer

2³ < 3²
Solution:
2³ _____ 3²
^$\because$ 2³ = 2 × 2 × 2 = 8
and 3² = 3 × 3 = 9
So, 8 < 9
$\therefore$ 2³ < 3²

View full question & answer→

Question 131 Mark

(-2)³¹ × (-2)¹³ = (-2)____.

Answer

(-2)³¹ × (-2)³¹ = (-2)⁴⁴
Solution:
Here, (-2)³¹ × (-2)³¹ = (-2)⁴⁴ $\big[\because\text{a}^{\text{m}\times\text{n}}=\text{a}^{\text{m+n}}\big]$
= (-2)⁴⁴
$\therefore$ (-2)³¹ × (-2)¹³ = (-2)⁴⁴

View full question & answer→

Question 141 Mark

27500000 = 2.75 × 10 _____.

Answer

27500000 = 2.75 × 10¹⁰
Solution:
Given, 27500000
For standard form, 27500000 = 275 × 10⁵ Also, 275
= 2.75 × 10²
So, 2.75 × 10² × 10⁵
= 2.75 × 10⁷ [$\therefore$ a^m × aⁿ = a^m+n]
27500000 = 2.75 × 10⁷

View full question & answer→

Question 151 Mark

1 million = 10 _____.

Answer

1 million = 10⁶
Solution:
Here, 1 million
= 1000000 = 10⁶
$\therefore$ 1 million = 10⁶

View full question & answer→

Question 161 Mark

1 lakh = 10 _____.

Answer

1 lakh = 10⁵
Solution:
Here, 1 lakh
= 100000 = 10⁵
$\therefore$ 1 lakh = 10⁵

View full question & answer→

Question 171 Mark