Question

(81×3^-5)^2вычеслите выражение

Answer 1

=(3^4*3^-5)^2=(3^-1)^2=3^-2=1/3²=1/9

Answer 2

To calculate the expression (81 × 3^(-5))^2, we'll follow the order of operations (PEMDAS/BODMAS) which dictates that we should first evaluate the exponent, then perform the multiplication, and finally square the result.

Let's break it down step by step:

Step 1: Evaluate the exponent 3^(-5) means "3 raised to the power of -5." When a number is raised to a negative exponent, it can be expressed as its reciprocal with the exponent made positive. So, 3^(-5) is equivalent to 1/(3^5) or 1/243.

Step 2: Perform the multiplication 81 × (1/243) = 81/243 = 1/3.

Step 3: Square the result (1/3)^2 = 1^2 / 3^2 = 1/9.

Therefore, the value of the expression (81 × 3^(-5))^2 is 1/9.