Question

6^11×6^-99^-4:9^-2(2^-3)^2​

Answer 1

Пошаговое объяснение:

6¹¹ * 6-⁹ = 6^(11-9) = 6² = 36

9-⁴ : 9-² = 9^(-4-(-2)) = 9^(-4+2) = 9-² = 1/(9²) = 1/81

(2-³)² = 2-⁶ = 1/(2⁶) = 1/64

Answer 2

To simplify the expression, let's break it down step by step.

First, let's simplify the exponent terms:

6^11 × 6^-99^-4 = 6^(11 + (-99) * (-4))

Since any number raised to the power of -4 is the reciprocal of that number raised to the power of 4, we have:

6^(11 + (-99) * (-4)) = 6^(11 + 396) = 6^407

Next, let's simplify the second part of the expression:

9^-2(2^-3)^2 = 9^(-2) × (2^(-3))^2

Since any number raised to the power of -2 is the reciprocal of that number raised to the power of 2, and squaring a number squared exponent is the same as multiplying the exponents, we have:

9^(-2) × (2^(-3))^2 = (1/9^2) × (2^(-3 × 2))

Simplifying further:

(1/9^2) × (2^(-3 × 2)) = (1/81) × (2^(-6)) = 1/81 × 1/(2^6) = 1/(81 × 64) = 1/5184

Now we can combine the results:

6^407 × 1/5184 = (6^407)/(5184)

This is the simplified form of the given expression: (6^407)/(5184).