What if Damayanti had changed the order in which she placed the flowers in the lakes? Class 8

What if Damayanti had changed the order in which she placed the flowers in the lakes? Class 8

Question 1.

What if Damayanti had changed the order in which she placed the flowers in the lakes? How many lotuses would be there? Class 8

1 × 3⁴ × 2⁴ = (3 × 3 × 3 × 3) × (2 × 2 × 2 × 2).

Solution:

(3 × 2)⁴ = 6⁴.

Question 2.

Can this product be expressed as an exponent mⁿ, where m and n are some counting numbers? Class 8

By regrouping the numbers,

= (3 × 2) × (3 × 2) × (3 × 2) × (3 × 2)

= (3 × 2)⁴ = 6⁴.

In general form,

m^a × n^a = (mn)^a, where a is a counting number.

Use this observation to compute the value of 2⁵ × 5⁵.

Solution:

Yes, 6⁴.

Question 3.

Simplify [latex]\frac{10^4}{5^4}[/latex]and write it in exponential form. Class 8

In general, we can show that [latex]\frac{m^a}{n^a}=\left(\frac{m}{n}\right)^a[/latex].

Solution:

[latex]\frac{10^4}{5^4}=\frac{10 \times 10 \times 10 \times 10}{5 \times 5 \times 5 \times 5}[/latex]

= 2 × 2 × 2 × 2

= 2⁴