We had required a and b to be counting numbers. Can a and b be any integers? Will the generalised forms still hold true? Class 8

We had required a and b to be counting numbers. Can a and b be any integers? Will the generalised forms still hold true? Class 8

Question 1.

We had required a and b to be counting numbers. Can a and b be any integers? Will the generalised forms still hold true? Class 8 Solution: Yes; yes.

Question 2.

Write equivalent forms of the following, Class 8 (i) 2^-4

(ii) 10^-5

(iii) (- 7)^-2

(iv) (-5)^-3

(v) 10^-100

Solution:

(i) 2^-4 = [latex]\frac{1}{2^4}[/latex]

(ii) 10^-5 = [latex]\frac{1}{10^5}[/latex]

(iii) (-7)^-2 = [latex]\frac{1}{(-7)^2}[/latex]

(iv) (-5)^-3 = [latex]\frac{1}{(-5)^3}[/latex]

(v) 10^-100 = [latex]\frac{1}{10^{100}}[/latex]

Question 3.

Simplify and write the answers in exponential form. Class 8

(i) 2^-4 × 2⁷

(ii) 3² × 3^-5 × 3⁶

(iii) p³ × p^-10

(iv) 2⁴ × (-4)^-2

(v) 8^p × 8^q

Solution:

(i) 2^-4 × 2⁷ = [latex]\frac{7}{2^4}[/latex] = 2^7-4 = 2³.

(ii) 3² × 3^-5 × 3⁶ = [latex]\frac{3^2}{3^5}[/latex] × 3⁶ = 3^3+6-5 = 3³.

(iii) p³ × p^-10 = p^3-10 = p^-7.

(iv) 2⁴ × (-4)^-2 = 2⁴ × (-2²)^-2= 2⁴ × (-2)^-4

= [latex]\frac{2^4}{(-2)^4}=\frac{2^4}{2^4}[/latex] = 1.

(v) 8^p × 8^q

= 8^p+q