Question

Express 27 x 27 x 27 in exponential form with base 3

Answer 1

3^9

Explanation:

27x27x27

27=3x3x3

Substitute 3x3x3 in for 27

(3x3x3)x(3x3x3)x(3x3x3)

=3x3x3x3x3x3x3x3x3

There are nine 3's

so 3^9

Answer 2

`3^(9)`

Explanation:

using the rule of exponents

•
`a^(m)` ×
`a^(n)` =
`a^((m+n))`

this rule can be extended to any number of products with the same base.

note that 27 = 3³ ← in base 3

given

27 × 27 × 27 ← express in exponential form

= 3³ × 3³ × 3³

=
`3^((3+3+3))`

=
`3^(9)`