Chapter 11: Exponents and Powers

Solution:-

a⁶ × a⁵ × a⁰ = a¹¹

We know that,

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m × aⁿ × a^o= a^m+n+o

a⁶ × a⁵ × a⁰ = a^{5 + 6 + 0}

= a¹¹

Solution: –

1 lakh = 10⁵

Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific notation.

1 lakh = 1,00,000

= 10⁵

Solution:-

1 million = 10⁶

Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific notation.

1 million = 10,00,000

= 10⁶

Solution: –

729 = 3⁶

Now, we have to find out the factors of 729.

Therefore, factors of 729 are = 3 × 3 × 3 × 3 × 3 × 3

729 = 3⁶

Solution:-

432 = 2⁴ × 3³

Now, we have to find out the factors of 432.

Therefore, factors of 432 are = 2 × 2 × 2 × 2 × 3 × 3 × 3

432 = 2⁴ × 3³

Solution:-

53700000 = 5.37 × 10⁷

= (53700000/10000000) × 10000000

= 5.37 × 10⁷

Any number can be expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10. Such form of a number is called its standard form or scientific notation

Solution:-

88880000000 = 8.888 × 10¹⁰

= (88880000000/10000000000) × 10000000000

= 8.888 × 10¹⁰

Solution:-

27500000 = 2.75 × 10⁷

= (27500000/10000000) × 10000000

= 2.75 × 10⁷

Solution:-

340900000 = 3.409 × 10⁸

= (340900000/100000000) × 100000000

= 3.409 × 10⁸

Solution:-

3² < 15

Where, 3² = 3 × 3 = 9

Therefore, 9 < 15

(b) 2³ ______ 3²

Solution:-

2³ < 3²

Where, 2³ = 2 × 2 × 2 = 8

3² = 3 × 3 = 9

Therefore, 8 < 9

(c) 7⁴ ______5⁴

Solution:-

7⁴ > 5⁴

Where, 7⁴ = 7 × 7 × 7 × 7 = 2401

5 × 5 × 5 × 5 = 625

Therefore, 2401 > 625

(d) 10,000 ______ 10⁵

Solution:-

10,000 < 100000

Where, 10 × 10 × 10 × 10 × 10= 100000

Therefore, 10,000 < 100000

(e) 6³ _____4⁴

Solution:-

6³ < 4⁴

Where, 6³ = 6 × 6 × 6 = 216

4⁴ = 4 × 4 × 4 × 4 = 256

Therefore, 216 < 256

In questions 41 to 50, state whether the given statements are True or False.