Question

Simplify using the laws of exponents (3^2 x 3^3)^2

3^10

3^12

3^8

3^7

Answer 1

To simplify the given expression using the laws of exponents, we combine the exponents inside the parentheses, calculate the value, and simplify the denominators. The final answer is 81.

Step-by-step explanation:

To simplify the given expression, (3^2 x 3^3)^2 ÷ 3^10 x 3^12 ÷ 3^8 x 3^7, we can apply the laws of exponents. Let's break it down step by step:

1. For (3^2 x 3^3)^2, we can combine the exponents inside the parentheses by adding them together. This gives us 3^(2 + 3)^2.
2. Next, we can simplify the expression (3^2 x 3^3)^2 to 3^5^2.
3. Now, we can calculate 3^5, which is 243.
4. For the denominators, we can combine the exponents by subtracting them. So, we have 3^(12 - 10) ÷ 3^(8 - 7).
5. Simplifying further, we get 3^2 ÷ 3^1, which is equal to 3.
6. Finally, we can multiply the numerators and divide by the denominator. Thus, the simplified expression is 243 ÷ 3, which equals 81.