Question

(3^3×3^5)^6/(3×3^8)^5

Answer 1

Ответ:

Решение на фото во вложении.

Answer 2

Ответ:

(3^3×3^5)^6       3^48

------------------- = ------------------ = 3^3=27

(3×3^8)^5            3^45

Объяснение:

Answer 3

To simplify the expression (3^3 × 3^5)^6 / (3 × 3^8)^5, let's break it down step by step.

First, let's simplify the numerator (3^3 × 3^5)^6:

Using the properties of exponents, we can multiply the exponents when the bases are the same, so we have: 3^3 × 3^5 = 3^(3+5) = 3^8

Now, we have (3^8)^6 in the numerator.

Applying the power of a power rule, we multiply the exponents: (3^8)^6 = 3^(8×6) = 3^48

Moving on to the denominator, let's simplify (3 × 3^8)^5:

Again, using the properties of exponents, we multiply the exponents when the bases are the same, so we have: 3 × 3^8 = 3^(1+8) = 3^9

Now, we have (3^9)^5 in the denominator.

Applying the power of a power rule, we multiply the exponents: (3^9)^5 = 3^(9×5) = 3^45

Finally, we can rewrite the expression as:

(3^3 × 3^5)^6 / (3 × 3^8)^5 = 3^48 / 3^45

Now, to divide the two powers with the same base, we subtract the exponents:

3^48 / 3^45 = 3^(48-45) = 3^3 = 27

Therefore, the simplified expression is 27.