Question

81× 6(-4 степень) ×21(-5 степень) /14(-5 степень)

Answer 1

81=9^2=3^4
21=3*7
14=2*7
6=2*3
3^4*2^-4*3^-4*3^-5*7^-5/2^-5*7^-5 (7^-5 сокращаются)
3^4*2^-4*3^-4*3^-5/2^-5 (2^-4 сокращается с 2^-5, от 2^-5 остается 2^-1, 2^-1=1/2 но так как 2^-1 находится в знаменателе,то 2^-1=2)
3^4*3^-4*3^-5*2 (3^4*3^-4=1 т, к, они противоположны)
3^-5*2= 2/243

Answer 2

To calculate the expression, let's break it down step by step:

1. Start with the multiplication: 81 × 6. 81 × 6 = 486.

2. Next, raise 6 to the power of -4: 6^(-4) = 1 / (6^4) = 1 / 1296 ≈ 0.0007716.

3. Raise 21 to the power of -5: 21^(-5) = 1 / (21^5) = 1 / 4084101 ≈ 2.448 × 10^(-7).

4. Raise 14 to the power of -5: 14^(-5) = 1 / (14^5) = 1 / 537824 ≈ 1.859 × 10^(-6).

5. Now, divide the results from steps 2, 3, and 4: (0.0007716 × 2.448 × 10^(-7)) / (1.859 × 10^(-6)).

To simplify this expression, we can multiply the numerator and denominator by the reciprocal of the denominator:

(0.0007716 × 2.448 × 10^(-7)) / (1.859 × 10^(-6)) = (0.0007716 × 2.448 × 10^(-7)) × (1 / (1.859 × 10^(-6))) = (0.0007716 × 2.448) × (10^(-7) / (1.859 × 10^(-6))) = 0.0018899968 × (10^(-7 - (-6))) = 0.0018899968 × 10^(-7 + 6) = 0.0018899968 × 10^(-1) = 0.00018899968.

Therefore, 81 × 6^(-4) × 21^(-5) / 14^(-5) is approximately equal to 0.00018899968.