Question

Evaluate:

27ⁿ × 3^{2 – 3n}

Answer 1

Given:

27ⁿ × 3^{2 – 3n}

i. Express 27 as a power of 3:

The number 27 can be written as 3³. Therefore, 27ⁿ can be written as (3³)ⁿ.

ii. Simplify the expression using the power rule of exponents:

Using the rule (a^m)ⁿ = a^{m × n}, we get (3³)ⁿ = 3³ⁿ.

The original expression now becomes 3³ⁿ × 3^{(2 − 3n)}.

iii. Combine the terms using the product rule of exponents:

Using the rule a^m × aⁿ = a^{(m + n)}, we can add the exponents of the terms.

The new exponent will be 3n + (2 − 3n).

3n + 2 - 3n = 2

The expression simplifies to 3².

iv. Calculate the final value:

The value of 3² is 3 × 3 = 9