**GSEB Solutions for Class 7 Mathematics – Power and Exponent (English Medium)**

GSEB SolutionsMathsScience

**Exercise**

**Solution 1:**

**Solution 2:**

**Solution 3(1):**

[(3^{5})^{3} ÷ (3^{2})^{2}] ÷ 3^{8}

= [3^{5×3} ÷ 3^{2×2}]÷ 3^{8}

= [3^{15} ÷ 3^{4}]÷3^{8}

= [3^{15-4}]÷ 3^{8}

= 3^{11-8}

= 3^{3}

= 27

**Solution 3(2):**

**Solution 3(3):**

**Solution 3(4):**

**Solution 3(5):**

**Solution 3(6):**

**Solution 4(1):**

**Solution 4(2):**

**Solution 4(3):**

**Solution 4(4):**

**Solution 4(5):**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Practice – 1**

**Solution 1:**

**Solution 2(1):**

**Solution 2(2):**

**Solution 2(3):**

**Solution 2(4):**

**Solution 2(5):**

**Solution 3(1):**

**Solution 3(2):**

**Solution 3(3):**

**Solution 3(4):**

y^{12} ÷ (y^{6} × y^{3} × y)

= y^{12} ÷ (y^{6+3+1})

= y^{12} ÷ (y^{10})

= y^{12-10 }

= y^{2}

**Solution 3(5):**

x^{10} ÷ (x^{2 }× x^{3} ÷ x)

= x^{10} ÷ (x^{2+3} ÷ x)

= x^{10} ÷ (x^{5} ÷ x)

= x^{10} ÷ ( x^{5-1})

= x^{10} ÷ x^{4}

= x^{10-4}

= x^{6}

**Solution 3(6):**

(y^{6} ÷ y^{4}) × (y^{2 }× y^{3})

= (y^{6-4}) × (y^{2+3})

= y^{2} × y^{5}

= y^{2+5}

= y^{7}

**Solution 4:**

x × x^{2} × x^{3}

= x^{1+2+3}

= x^{6}

Substituting x = 2, we have

x^{6} = 2^{6}

∴ x^{6} = 64

∴ x× x^{2} × x^{3} = 64

x^{8 }÷ x^{7} × x^{2}

= x^{8-7 }× x^{2}

= x^{1} × x^{2}

= x^{1+2}

= x^{3}

Substituting x = 2, we have

x^{3} = 2^{3} = 8

∴ x^{8 }÷ x^{7} × x^{2} = 8

**Solution 5:**

x^{15 }÷ (x^{17} ÷ x^{6})

= x^{15 }÷ (x^{17-6})

= x^{15 }÷ (x^{11})

= x^{15 – 11}

= x^{4}

Substituting x = (-3), we have

x^{4} = (-3)^{4} = (81)

(When a negative number is raised to an even power, the result is positive)

∴ x^{15 }÷ (x^{17} ÷ x^{6}) = 81

(x^{6 }× x^{4}) ÷ (x^{2} × x^{3})

= (x^{6+4}) ÷ (x^{2+3})

= (x^{10}) ÷ (x^{5})

= x^{10 – 5}

= x^{5}

Substituting x = (-3), we have

x^{5} = (-3)^{5} = (-243)

(When a negative number is raised to an odd power, the result is negative)

∴ (x^{6 }× x^{4}) ÷ (x^{2} × x^{3}) = (-243)

**Practice – 2**

**Solution 1:**

**Solution 2(1):**

**Solution 2(2):**

2^{6} × 2^{2} × 2^{5} ÷ 8^{3}

= 2^{6+2+5} ÷ (2^{3})^{3}

= 2^{13} ÷ 2^{9}

= 2^{13 – 9}

= 2^{4}

= 16^{ }

**Solution 2(3):**

**Solution 2(4):**

**Solution 2(5):**