𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Write in exponential form (3/10)⁵ x (2/15)⁵ ?

𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

Using the rule of exponents:

a^n × b^n = (a × b)^n

(3/10)^5 × (2/15)^5 = [(3/10) × (2/15)]⁵

Now, simplify the expression inside the brackets:

(3/10) × (2/15) = (3 × 2) / (10 × 15) = 6 / 150

Simplify the fraction 6/150 by dividing both numerator and denominator by their greatest common divisor, which is 6:

6 / 6 = 1

150 / 6 = 25

So, (3/10) × (2/15) = 1/25

Now, write 1/25 in exponential form with base 5:

1/25 = 1/5² = 5⁻²

Therefore, the expression becomes:

(1/25)⁵ = (5⁻²)⁵ = 5^(⁻² × ⁵) = 5⁻¹⁰

Exponential form: 5⁻¹⁰