Question

Which is the value of this expression when a = 5 and k = negative 2?

(StartFraction 3 squared a Superscript negative 2 Baseline Over 3 a Superscript negative 1 Baseline EndFraction) Superscript k

Answer 1

To find the value of the given expression, substitute the values of a = 5 and k = -2 into the expression and evaluate the numerator and denominator separately. Then, apply the exponent k = -2 to the fraction.

Step-by-step explanation:

To find the value of the expression (3²a⁻²)/(3a⁻¹)ᵏ when a = 5 and k = -2, we substitute the given values of a and k into the expression.

First, let's evaluate the numerator (3²a⁻²). Substitute a = 5 into the expression: (3²·5⁻²) = (3²/5²) = 9/25.

Next, let's evaluate the denominator (3a⁻¹). Substitute a = 5 into the expression: 3·5⁻¹ = 3/5.

Now, substitute the values of the numerator and denominator into the expression and apply the exponent k = -2: (9/25)ᵏ = (9/25)⁻² = (25/9)² = 625/81.