**GSEB Solutions for Class 7 Mathematics – Revision 1 (Sem – II) (English Medium)**

GSEB SolutionsMathsScience

**Revision 1**

**Solution 1(1):**

c. 5^{6}

[(-5)^{2}]^{3}

= (-5)^{2×3}

=(-5)^{6}

= 5^{6}

Hint: When a negative number is raised by an even number, the product is always positive.

**Solution 1(2):**

b. x^{5}

x^{3} × x^{2}

= x^{3 + 2}

= x^{5}

**Solution 1(3):**

**Solution 1(4):**

a. 2^{3}

(-12)^{3}

= (-6 × 2)^{3}

= (-6)^{3} × 2^{3}

**Solution 1(5):**

a. 7^{6}

7^{12} ÷ (7^{3})^{2}

= 7^{12} ÷ (7^{3×2})

= 7^{12} ÷ 7^{6}

= 7^{12-6}

= 7^{6}

**Solution 1(6):**

b. a^{12}b^{6}c^{3}

(a^{4}b^{2}c)^{3}

= (a^{4×3})(b^{2×3})(c^{3})

= a^{12}b^{6}c^{3}

**Solution 1(7):**

**Solution 1(8):**

b. m^{3}n^{3}

m^{2}n × n^{2}m

= m^{2+1} × n^{1+2}

= m^{3}n^{3}

**Solution 2(1):**

m^{4} × m^{5} ÷ m^{3} (m ≠ 0)

= m^{4+5} ÷ m^{3}

= m^{9} ÷ m^{3}

= m^{9 – 3 }

= m^{6}

**Solution 2(2):**

a^{10} ÷ a^{13} × a (a ≠ 0)

= a^{10-13} × a

= a^{-3} × a

= a^{-3+1}

= a^{-2}

= 1/a^{2}

**Solution 2(3):**

(xy)^{3} ÷ [x^{4} × (y^{2})^{3}] (x ≠ 0, y ≠ 0)

= x^{3}y^{3} ÷ [x^{4} × (y^{2×3})]

= x^{3}y^{3} ÷ x^{4}y^{6}

= x^{3-4}y^{3-6}

= x^{-1}y^{-3}

= 1/xy^{3}

**Solution 3(1):**

3^{6 }× (3^{3})^{2} ÷ 3^{10}

= 3^{6 }× 3^{3×2} ÷ 3^{10}

= 3^{6 }× 3^{6} ÷ 3^{10}

= 3^{6+6 }÷ 3^{10}

= 3^{12-10}

= 3^{2}

= 9

**Solution 3(2):**

[(-5)^{3 }]^{3} ÷ [(-5)^{2}]^{3}

= (-5)^{3×3} ÷ (-5)^{2×3}

= (-5)^{9} ÷ (-5)^{6}

= (-5)^{9-6}

= (-5)^{3}

= (-5) × (-5) × (-5)

= (-125)

**Solution 3(3):**

**Solution 3(4):**

(2^{2})^{6} ÷ (2^{2 }× 2^{4})

= 2^{2×6} ÷ (2^{2+4})

= 2^{12} ÷ (2^{6})

= 2^{12-6}

= 2^{6}

= 64

**Solution 4:**

**Solution 5(1):**

**Solution 5(2):**

**Solution 5(3):**

**Solution 6(1):**

10 – {10 + (6 ÷ 2)}

= 10 – {10 + 3}

= 10 – {13}

= 10 – 13

= (-3)

**Solution 6(2):**

5 × [7 + (4 × 3)]

= 5 × [7 + 12]

= 5 × [19]

= 5 × 19

= 95

**Solution 6(3):**

7y – [-{-(-7x)}]

= 7y – [-{7x}]

= 7y – [-7x]

= 7y +7x

**Solution 6(4):**

2a – {a + 2(5 – b)}

= 2a – {a + 10 – 2b}

= 2a – a – 10 + 2b

= a – 10 + 2b

= a + 2b – 10

**Solution 6(5):**

[3y – (x + 2y)] – [x + (2x – y)]

= [3y – x – 2y] – [x + 2x – y]

= [y – x] – [3x – y]

= y – x – 3x + y

= y + y – x – 3x

= 2y – 4x

**Solution 6(6):**

**Solution 6(7):**

[3a – a(2 – a)] – a

= [3a – 2a + a^{2}] – a

= [a + a^{2}] – a

= a + a^{2} – a

= a^{2}

**Solution 6(8):**

[(10 ÷ 5) ÷ (45 ÷ 9)]

= 2 ÷ 5

= 2/5

**Solution 6(9):**

{(7 × 2) – 4} – [8 – (10 ÷ 2)]

= {(14) – 4} – [8 – (5)]

= {10} – [3]

= 7

**Solution 6(10):**

m + [n + {2m – (m + 2n)}]

= m + [n + {2m – m – 2n}]

= m + [n + {m – 2n}]

= m + [n + m – 2n]

= m + [m – n]

= m + m – n

= 2m – n