What is the numerical equivalent of 9 to the 9th power times 9 to the -6th power
To find the numerical equivalent of 9 to the 9th power times 9 to the -6th power, we use the property of exponents which states that when a number is raised to a power, and then that result is raised to another power, we simply add the exponents.
Therefore, we have:
9^9 * 9^(-6) = 9^(9 + (-6))
The sum of the exponents is 9 + (-6) = 3.
So, the numerical equivalent is 9^3.
9^3 = 9 * 9 * 9 = 729.
Therefore, the numerical equivalent of 9 to the 9th power times 9 to the -6th power is 729.
To find the numerical equivalent of 9 to the 9th power times 9 to the -6th power, we can use the power of a power rule.
First, let's calculate 9 to the 9th power:
9^9 = 387,420,489
Next, let's calculate 9 to the -6th power:
9^(-6) = 1/9^6 = 1/531,441
Now, let's multiply these two results together:
387,420,489 * (1/531,441) = 0.729
Therefore, the numerical equivalent of 9 to the 9th power times 9 to the -6th power is 0.729.
To find the numerical equivalent of this expression, we can apply the rule of exponents which states that when you multiply two numbers with the same base, you add their exponents.
In this case, we have 9 to the 9th power multiplied by 9 to the -6th power. Let's break it down step by step:
1. Compute 9 to the 9th power:
9^9 = 387,420,489
2. Compute 9 to the -6th power:
Taking the reciprocal of a number raised to a negative exponent gives us the positive exponent of its reciprocal. In this case:
9^-6 = 1 / 9^6
Now, let's calculate 9^6:
9^6 = 531,441
Therefore, 9 to the -6th power is equal to 1 divided by 531,441:
9^-6 = 1 / 531,441
3. Multiply the results from steps 1 and 2:
387,420,489 * (1 / 531,441)
Evaluating this expression gives us:
730.024
Therefore, the numerical equivalent of 9 to the 9th power times 9 to the -6th power is approximately 730.024.