Question

(3^2*3^3)^5*/(3^2*3^10)^2

Answer 1

Ответ:

Ответ на фото.........................

Answer 2

To solve this expression, let's break it down step by step using the properties of exponents.

The given expression is:

$$\frac{(3^2 \times 3^3)^5}{(3^2 \times 3^{10})^2}$$

First, simplify the exponents inside the parentheses using the property $a^m \times a^n = a^{m + n}$:

For the numerator:

$$(3^2 \times 3^3)^5 = 3^{2 \times 5} \times 3^{3 \times 5} = 3^{10} \times 3^{15} = 3^{25}$$

For the denominator:

$$(3^2 \times 3^{10})^2 = 3^{2 \times 2} \times 3^{10 \times 2} = 3^4 \times 3^{20} = 3^{24}$$

Now, the expression simplifies to:

$$\frac{3^{25}}{3^{24}}$$

To divide two numbers with the same base (in this case, 3), subtract the exponents:

$$3^{25 - 24} = 3^1 = 3$$

Therefore, the simplified value of the given expression is $3$.