Question
Use the Product Rule of Exponents to simplify the expression 7^5 ⋅ 7^2.
Answers
Answer
Find the numerical equivalent of 7^2 ⋅ 7^3
Answer
Find the numerical equivalent of 3^9 ⋅ 3^−5
Answered by
GPT 3.5
The Product Rule of Exponents states that for any real number a and any integers m and n, a^m⋅a^n = a^(m+n).
Using this rule, we can simplify the expression 7^5 ⋅ 7^2 as follows:
7^5 ⋅ 7^2 = 7^(5+2) = 7^7
Therefore, 7^5 ⋅ 7^2 simplifies to 7^7.
Using this rule, we can simplify the expression 7^5 ⋅ 7^2 as follows:
7^5 ⋅ 7^2 = 7^(5+2) = 7^7
Therefore, 7^5 ⋅ 7^2 simplifies to 7^7.
Answered by
GPT 3.5
To find the numerical equivalent of 7^2 ⋅ 7^3, we can simplify each exponent separately and then multiply the results.
7^2 = 7 * 7 = 49
7^3 = 7 * 7 * 7 = 343
Now, we can multiply the results:
49 * 343 = 16,807
Therefore, the numerical equivalent of 7^2 ⋅ 7^3 is 16,807.
7^2 = 7 * 7 = 49
7^3 = 7 * 7 * 7 = 343
Now, we can multiply the results:
49 * 343 = 16,807
Therefore, the numerical equivalent of 7^2 ⋅ 7^3 is 16,807.
Answered by
GPT 3.5
To find the numerical equivalent of 3^9 ⋅ 3^−5, we can simplify each exponent separately and then multiply the results.
3^9 is equal to 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3, which simplifies to 19683.
3^−5 is equal to 1 / (3^5), which simplifies to 1 / (3 * 3 * 3 * 3 * 3) = 1 / 243.
Now, we can multiply the results:
19683 * (1 / 243) = 19683 / 243 = 81.
Therefore, the numerical equivalent of 3^9 ⋅ 3^−5 is 81.
3^9 is equal to 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3, which simplifies to 19683.
3^−5 is equal to 1 / (3^5), which simplifies to 1 / (3 * 3 * 3 * 3 * 3) = 1 / 243.
Now, we can multiply the results:
19683 * (1 / 243) = 19683 / 243 = 81.
Therefore, the numerical equivalent of 3^9 ⋅ 3^−5 is 81.