Question

Simplify the following (i) 3(a4 b3 ) 10 x 5 (a2 b2 ) 3

Answer 1

To simplify the given expression, apply the rule of exponents to find 15a^46b^36.

Step-by-step explanation:

To simplify the expression 3(a4 b3)10 x 5 (a2 b2)3, we must use the rule of exponents which states that when an exponential term is raised to another power, we multiply the exponents. This is represented as (xa)b = xa · b.

First, apply this rule to each term individually:

• (a4)10 = a4 · 10 = a40
• (b3)10 = b3 · 10 = b30
• (a2)3 = a2 · 3 = a6
• (b2)3 = b2 · 3 = b6

Now, simplify the coefficients and combine like terms:

• Coefficients: 3 × 5 = 15

Combine like terms by adding the exponents of 'a' and 'b':

• a40 × a6 = a40 + 6 = a46
• b30 × b6 = b30 + 6 = b36

Therefore, our simplified expression is:

15a46b36