#### Chapters

## Chapter 3: Algebra

### Samacheer Kalvi solutions for Mathematics Term 2 - Class 7th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.1 [Pages 51 - 53]

#### Fill in the blanks

The exponential form 14^{9} should be read as _______________

The expanded form of p^{3} q^{2} is ________________

When base is 12 and exponent is 17, its exponential form is _____________

The value of (14 × 21)^{0} is _______________

#### Say True or False

2^{3} × 3^{2} = 6^{5}

True

False

2^{9} × 3^{2} = (2 × 3)^{9×2 }

True

False

3^{4} × 3^{7 }= 3^{11}

True

False

2^{0} × 1000^{0}

True

False

2^{3} < 3^{2}

True

False

Find the value of the following.

2^{6}

Find the value of the following.

11^{2}

Find the value of the following.

5^{4}

Find the value of the following.

9^{3}

Express the following in exponential form.

6 × 6 × 6 × 6

Express the following in exponential form.

t × t

Express the following in exponential form.

5 × 5 × 7 × 7 × 7

Express the following in exponential form.

2 × 2 × a × a

Express the following numbers using exponential form.

512

Express the following numbers using exponential form.

343

Express the following numbers using exponential form.

729

Express the following numbers using exponential form.

3125

Identify the greater number in the following.

6^{3} or 3^{6}

Identify the greater number in the following.

5^{3} or 3^{5}

Identify the greater number in the following.

2^{8} or 8^{2}

Simplify the following.

7^{2} × 3^{4 }

Simplify the following.

3^{2} × 2^{4}

Simplify the following.

5^{2} × 10^{4}

Find the value of the following.

(−4)^{2}

Find the value of the following.

(−3) × (−2)^{3}

Find the value of the following.

(−2)^{3} × (−10)^{3}

Simplify using law of exponents.

3^{5} × 3^{8}

Simplify using law of exponents.

a^{4} × a^{10}

Simplify using law of exponents.

7^{x} × 7^{2}

Simplify using law of exponents.

2^{5} ÷ 2^{3 }

Simplify using law of exponents.

18^{8} ÷ 18^{4}

Simplify using law of exponents.

(6^{4})^{3}

Simplify using law of exponents.

(x^{m})^{0}

Simplify using law of exponents.

9^{5} × 3^{5}

Simplify using law of exponents.

3^{y} × 12^{y }

Simplify using law of exponents.

25^{6} × 5^{6}

If a = 3 and b = 2, then find the value of the following.

a^{b} + b^{a}

If a = 3 and b = 2, then find the value of the following.

a^{a} – b^{b}

If a = 3 and b = 2, then find the value of the following.

(a + b)^{b}

If a = 3 and b = 2, then find the value of the following.

(a – b)^{a}

Simplify and express the following in exponential form:

4^{5} × 4^{2} × 4^{4 }

Simplify and express the following in exponential form:

(3^{2} × 3^{3})^{7}

Simplify and express the following in exponential form:

(5^{2} × 5^{8}) ÷ 5^{5}

Simplify and express the following in exponential form:

2^{0} × 3^{0} × 4^{0}

Simplify and express the following in exponential form:

`(4^5 xx "a"^8 xx "b"^3)/(4^3 xx "a"^5 xx "b"^2)`

#### Objective type questions

a × a × a × a × a is equal to

a

^{5}5

^{a}5a

a + 5

The exponential form of 72 is

7

^{2}2

^{7}2

^{2}× 3^{3}2

^{3}× 3^{2}

The value of x in the equation a^{13} = x^{3} × a^{10} is

a

13

3

10

How many zeros are there in 100^{10}?

2

3

10

20

2^{40} + 2^{40} is equal to

4

^{40}2

^{80}2

^{41}4

^{80}

### Samacheer Kalvi solutions for Mathematics Term 2 - Class 7th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.2 [Pages 56 - 57]

#### Fill in the blanks.

Unit digit of 124 × 36 × 980 is _____________

When the unit digit of the base and its expanded form of that number is 9, then the exponent must be ____________ power.

Match the following:

Group AExponential form |
Group BUnit digit of the number |

(i) 20^{10} |
(a) 6 |

(ii) 121^{11} |
(b) 4 |

(iii) 444^{41} |
(c) 0 |

(iv) 25^{100} |
(d) 1 |

(v) 716^{83} |
(e) 9 |

(vi) 729^{725} |
(f) 5 |

Find the unit digit of expanded form.

25^{23}

Find the unit digit of expanded form.

11^{10}

Find the unit digit of expanded form.

46^{15}

Find the unit digit of expanded form.

100^{12}

Find the unit digit of expanded form.

29^{21}

Find the unit digit of expanded form.

19^{12}

Find the unit digit of expanded form.

24^{25}

Find the unit digit of expanded form.

34^{16}

Find the unit digit of the following numeric expression.

114^{20} + 115^{21} + 116^{22}

Find the unit digit of the following numeric expression.

10000^{10000} + 11111^{11111}

#### Objective type questions

Observe the equation (10 + y)^{4} = 50625 and find the value of y

1

5

4

0

The unit digit of (32 × 65)^{0} is

2

5

0

1

The unit digit of the numeric expression 10^{71} + 10^{72 }+ 10^{73} is

0

3

1

2

### Samacheer Kalvi solutions for Mathematics Term 2 - Class 7th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.3 [Pages 61 - 62]

#### Fill in the blanks

The degree of the term a^{3}b^{2}c^{4}d^{2} is ___________

Degree of the constant term is ______________

The coefficient of leading term of the expression 3z^{2}y + 2x – 3 is _________

#### Say True or False

The degree of m^{2}n and mn^{2} are equal

True

False

7a^{2}b and −7ab^{2} are like terms

True

False

The degree of the expression −4x^{2} yz is −4

True

False

Any integer can be the degree of the expression

True

False

Find the degree of the following terms.

5x^{2}

Find the degree of the following terms.

−7ab

Find the degree of the following terms.

12pq^{2}r^{2}

Find the degree of the following terms.

−125

Find the degree of the following terms.

3z

Find the degree of the following expression.

x^{3} – 1

Find the degree of the following expression.

3x^{2} + 2x + 1

Find the degree of the following expression.

3t^{4} – 5st^{2} + 7s^{2}t^{2}

Find the degree of the following expression.

5 – 9y + 15y^{2} – 6y^{3}

Find the degree of the following expression.

u^{5} + u^{4}v + u^{3}v^{2} + u^{2}v^{3} + uv^{4}

Identify the like terms: 12x^{3}y^{2}z, – y^{3}x^{2}z, 4z^{3}y^{2}x, 6x^{3}z^{2}y, – 5y^{3}x^{2}z

Add and find the degree of the following expressions.

(9x + 3y) and (10x – 9y)

Add and find the degree of the following expressions.

(k^{2} – 25k + 46) and (23 – 2k^{2} + 21k)

Add and find the degree of the following expressions.

(3m^{2}n + 4pq^{2}) and (5nm^{2} – 2q^{2}p)

Simplify and find the degree of the following expression.

10x^{2} – 3xy + 9y^{2} – (3x^{2} – 6xy – 3y^{2})

Simplify and find the degree of the following expression.

9a^{4} – 6a^{3} – 6a^{4} – 3a^{2} + 7a^{3} + 5a^{2 }

Simplify and find the degree of the following expression.

4x^{2} – 3x – [8x – (5x^{2} – 8)]

#### Objective type questions

3p^{2} – 5pq + 2q^{2} + 6pq – q^{2} + pq is a

Monomial

Binomial

Trinomial

Quadrinomial

The degree of 6x^{7} – 7x^{3} + 4 is

7

3

6

4

If p(x) and q(x) are two expressions of degree 3, then the degree of p(x) + q(x) is

6

0

3

Undefined

### Samacheer Kalvi solutions for Mathematics Term 2 - Class 7th Tamil Nadu State Board Chapter 3 Algebra Exercise 3.4 [Pages 62 - 63]

#### Miscellaneous Practice problems

6^{2} × 6^{m} = 6^{5}, find the value of ‘m’

Find the unit digit of 124^{128} × 126^{124}

Find the unit digit of the numeric expression: 16^{23} + 71^{48} + 59^{61}

Find the value of `((-1)^6 xx (-1)^7 xx (-1)^8)/((-1)^3 xx (-1)^5)`

Identify the degree of the expression, 2a^{3}bc + 3a^{3}b + 3a^{3}c – 2a^{2}b^{2}c^{2}

If p = −2, q = 1 and r = 3, find the value of 3p^{2}q^{2}r

#### Challenge Problems

**LEADERS** is a WhatsApp group with 256 members. Every one of its member is an admin for their own WhatsApp group with 256 distinct members. When a message is posted in LEADERS and everybody forwards the same to their own group, then how many members in total will receive that message?

Find x such that 3^{x+2} = 3^{x} + 216

If X = 5x^{2} + 7x + 8 and Y = 4x^{2} – 7x + 3, then find the degree of X + Y

Find the degree of (2a^{2} + 3ab – b^{2}) – (3a^{2} – ab – 3b^{2})

Find the value of w, given that x = 3, y = 4, z = – 2 and w = x^{2} – y^{2} + z^{2} – xyz

Simplify and find the degree of 6x^{2} + 1 – [8x – {3x^{2} – 7 – (4x^{2} – 2x + 5x + 9)}]

The two adjacent sides of a rectangle are 2x^{2} – 5xy + 3z^{2} and 4xy – x^{2} – z^{2}. Find the perimeter and the degree of the expression

## Chapter 3: Algebra

## Samacheer Kalvi solutions for Mathematics Term 2 - Class 7th Tamil Nadu State Board chapter 3 - Algebra

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