Question

1)2×3^3/3^2; 2) 2^4×3^2/2^3×3 3) 3^5×3^10/3^6×3^7 4) 5^8×5^7/5^4×5^9

Answer 1

Вроде как должно быть так
1) 6
2) 6
3) 9
4) 25

Answer 2

To simplify each of these expressions, we'll follow the rules of exponents, which state that when you have the same base raised to different exponents, you can simplify by adding or subtracting the exponents. Let's go through each expression:

1. 2×3^3/3^2 Since the base is the same (3), we can subtract the exponents: 2 × 3^(3-2) = 2 × 3^1 = 2 × 3 = 6

2. 2^4×3^2/2^3×3 Here, we have two different bases, 2 and 3, so we cannot combine them. Let's first simplify the exponents with the same base: 2^4 / 2^3 = 2^(4-3) = 2^1 = 2 3^2 / 3 = 3^(2-1) = 3^1 = 3

Now, we have: 2 × 3

Therefore, the result is 2 × 3 = 6

3. 3^5×3^10/3^6×3^7 Again, the base is the same (3), so we can combine the exponents: 3^(5+10) / 3^(6+7) = 3^15 / 3^13

Since the base is the same, we subtract the exponents: 3^(15-13) = 3^2 = 9

4. 5^8×5^7/5^4×5^9 Once more, the base is the same (5), so we can simplify the exponents: 5^(8+7) / 5^(4+9) = 5^15 / 5^13

Again, since the base is the same, we subtract the exponents: 5^(15-13) = 5^2 = 25

So the final result is 25.