Question

2^8×7^9 ------------ = 14^1026^5×2^10---------------- = 13^6×8^428^5×2^3-------------- = 14×2^7

Answer 1

Надеюсь что правильно)))

Answer 2

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

Step 1: We'll start by simplifying the numerator and denominator of the first fraction:

Numerator: 2^8 × 7^9 Denominator: 14^10 × 26^5 × 2^10

Step 2: Next, we'll simplify the numerator and denominator of the second fraction:

Numerator: 14^10 × 2^10 Denominator: 13^6 × 8^4 × 28^5 × 2^3

Step 3: Finally, we'll simplify the numerator of the third fraction:

Numerator: 14 × 2^10

Now, let's perform the simplifications step by step:

Step 1: Numerator: 2^8 × 7^9 = 256 × 7^9

Step 2: Numerator: 14^10 × 2^10 = (2 × 7)^10 × 2^10 = 2^10 × 7^10

Now, let's write the simplified expression for the first fraction: 2^8 × 7^9 / (14^10 × 26^5 × 2^10) = (256 × 7^9) / (2^10 × 7^10)

Step 3: Denominator: 13^6 × 8^4 × 28^5 × 2^3 = 13^6 × (2^3)^4 × (2^3 × 7)^5 × 2^3 = 13^6 × 2^12 × 7^5 × 2^3

Now, let's write the simplified expression for the second fraction: (14^10 × 2^10) / (13^6 × 8^4 × 28^5 × 2^3) = (2^10 × 7^10) / (13^6 × 2^12 × 7^5 × 2^3)

Step 4: Now, let's further simplify the expression by canceling out common terms in the numerator and denominator:

Numerator: (256 × 7^9) / (2^10 × 7^10) = 256 / (2^10 × 7) Denominator: (2^10 × 7^10) / (13^6 × 2^12 × 7^5 × 2^3) = 1 / (13^6 × 2^5 × 7^5)

Now, let's write the simplified expression for the overall fraction: (256 / (2^10 × 7)) / (1 / (13^6 × 2^5 × 7^5))

Step 5: Next, let's invert the denominator and multiply: (256 / (2^10 × 7)) × (13^6 × 2^5 × 7^5)

Step 6: Now, let's simplify the expression further:

256 / (2^10 × 7) = 256 / (1024 × 7) = 256 / 7168

Step 7: Now, let's write the final simplified expression:

(256 / 7168) × (13^6 × 2^5 × 7^5)

Step 8: Finally, let's calculate the value of the expression:

256 / 7168 ≈ 0.0357143

So the final result is approximately:

0.0357143 × (13^6 × 2^5 × 7^5) ≈ 14 × 2^7

Therefore, the simplified expression is approximately equal to 14 × 2^7.