Question

Raj is simplifying (5^4)^3 using these steps:

(5^4)3 =5^4 x 5^4 x 5^4= 5^4+4+4

Although Raj is correct so far what could he have done instead to simplify the expression (5^4)^3 ?

Answer 1

`(a^(x))^(y)= a^(x*y) \\ \\So, (5^(4))^(3)= 5^(4*3) = 5^(12)`

Answer 2

Instead of simplifying the expression using the given steps Raj could directly apply property of exponents

`(5^4)^3=5^(12)`

Explanation:

Given raj has an expression
`(5^4)^3` and he simplifies this using the given steps.

He can do the following steps to simplify the above expression

Consider the given expression
`(5^4)^3`

Using property of exponents,
`(a^m)^n=a^(m\cdot n)`

Thus, the given expression beecomes,

`(5^4)^3=5^(4 \cdot 3)=5^(12)`

Thus, raj obtained the same answer only his calculation reduces,

`(5^4)^3=5^(12)`

Instead of simplifying the expression using the given steps Raj could directly apply property of exponents