To simplify the expression using the law of exponents, we can subtract the exponents since the base is the same. Therefore, 81^(10/12) / 81^(7/12) simplifies to 81^(10/12 - 7/12). Simplifying further, we get 81^(3/12), which is equivalent to 81^(1/4).
To simplify the expression using the law of exponents, we can subtract the exponents since the base is the same. Therefore, 81^(10/12) / 81^(7/12) simplifies to 81^(10/12 - 7/12). Simplifying further, we get 81^(3/12), which is equivalent to 81^(1/4).
To simplify the expression using the law of exponents, we can subtract the exponents since the base is the same. Therefore, 81^(10/12) / 81^(7/12) simplifies to 81^(10/12 - 7/12). Simplifying further, we get 81^(3/12), which is equivalent to 81^(1/4). Let's simplify the expression step by step using the law of exponents.
To simplify the expression using the law of exponents, we can subtract the exponents since the base is the same. Therefore, 81^(10/12) / 81^(7/12) simplifies to 81^(10/12 - 7/12). Simplifying further, we get 81^(3/12), which is equivalent to 81^(1/4). Let's simplify the expression step by step using the law of exponents. First, let's focus on the numerator, 81^(10/12). To simplify this, we can rewrite 81 as 3^4 since 81 is equal to 3 * 3 * 3 * 3.
To simplify the expression using the law of exponents, we can subtract the exponents since the base is the same. Therefore, 81^(10/12) / 81^(7/12) simplifies to 81^(10/12 - 7/12). Simplifying further, we get 81^(3/12), which is equivalent to 81^(1/4). Let's simplify the expression step by step using the law of exponents. First, let's focus on the numerator, 81^(10/12). To simplify this, we can rewrite 81 as 3^4 since 81 is equal to 3 * 3 * 3 * 3. So, 81^(10/12) becomes (3^4)^(10/12). According to the law of exponents, when we raise an exponent to another exponent, we multiply the exponents.
To simplify the expression using the law of exponents, we can subtract the exponents since the base is the same. Therefore, 81^(10/12) / 81^(7/12) simplifies to 81^(10/12 - 7/12). Simplifying further, we get 81^(3/12), which is equivalent to 81^(1/4). Let's simplify the expression step by step using the law of exponents. First, let's focus on the numerator, 81^(10/12). To simplify this, we can rewrite 81 as 3^4 since 81 is equal to 3 * 3 * 3 * 3. So, 81^(10/12) becomes (3^4)^(10/12). According to the law of exponents, when we raise an exponent to another exponent, we multiply the exponents. So, (3^4)^(10/12) simplifies to 3^(4 * 10/12) which is 3^(40/12).
Next, let's move on to the denominator, 81^(7/12). Using the same process, we can rewrite 81 as 3^4.
Next, let's move on to the denominator, 81^(7/12). Using the same process, we can rewrite 81 as 3^4. So, 81^(7/12) becomes (3^4)^(7/12). Applying the law of exponents, we have 3^(4 * 7/12) which is 3^(28/12).
Next, let's move on to the denominator, 81^(7/12). Using the same process, we can rewrite 81 as 3^4. So, 81^(7/12) becomes (3^4)^(7/12). Applying the law of exponents, we have 3^(4 * 7/12) which is 3^(28/12). Now, we can simplify the expression further by subtracting the exponents since the base is the same.
Next, let's move on to the denominator, 81^(7/12). Using the same process, we can rewrite 81 as 3^4. So, 81^(7/12) becomes (3^4)^(7/12). Applying the law of exponents, we have 3^(4 * 7/12) which is 3^(28/12). Now, we can simplify the expression further by subtracting the exponents since the base is the same. 3^(40/12) / 3^(28/12) simplifies to 3^(40/12 - 28/12) which is 3^(12/12).
Next, let's move on to the denominator, 81^(7/12). Using the same process, we can rewrite 81 as 3^4. So, 81^(7/12) becomes (3^4)^(7/12). Applying the law of exponents, we have 3^(4 * 7/12) which is 3^(28/12). Now, we can simplify the expression further by subtracting the exponents since the base is the same. 3^(40/12) / 3^(28/12) simplifies to 3^(40/12 - 28/12) which is 3^(12/12). Lastly, 3^(12/12) is equal to 3^1 which is simply 3.
Next, let's move on to the denominator, 81^(7/12). Using the same process, we can rewrite 81 as 3^4. So, 81^(7/12) becomes (3^4)^(7/12). Applying the law of exponents, we have 3^(4 * 7/12) which is 3^(28/12). Now, we can simplify the expression further by subtracting the exponents since the base is the same. 3^(40/12) / 3^(28/12) simplifies to 3^(40/12 - 28/12) which is 3^(12/12). Lastly, 3^(12/12) is equal to 3^1 which is simply 3. So, the simplified expression is 3.