Find the numerical equivalent (the answer) of 9^9 x 9^-6
To find the numerical equivalent of 9^9 × 9^-6, we can simplify the expression using the exponent rules.
9^9 can be written as (3^2)^9, which is equal to 3^(2×9) = 3^18.
Similarly, 9^-6 can be written as (3^2)^-6, which is equal to 3^(2×-6) = 3^-12.
Now, we can combine these simplified expressions:
3^18 × 3^-12 = 3^(18 + (-12)) = 3^6
Therefore, the numerical equivalent of 9^9 × 9^-6 is 3^6.
What is the missing exponent in the following equation?
h^450/h^? = h^215
To solve for the missing exponent, we can use the exponent rule for division. According to this rule, when dividing two terms with the same base, we subtract the exponents:
h^450/h^x = h^(450 - x) = h^215.
So, we need to solve the equation 450 - x = 215 to find the value of x.
Subtracting 450 from both sides, we have:
450 - x - 450 = 215 - 450,
-x = -235.
Now, we multiply both sides by -1 to solve for x:
x = 235.
Therefore, the missing exponent in the equation h^450/h^? = h^215 is 235.
To find the numerical equivalent of 9^9 x 9^-6, we can simplify the expression first. The rule for multiplying numbers with the same base is to add their exponents.
9^9 x 9^-6 can be rewritten as 9^(9+(-6)). Simplifying the exponents, we have 9^3.
To calculate 9^3, we multiply 9 by itself three times: 9 x 9 x 9.
9 x 9 = 81
81 x 9 = 729
Therefore, the numerical equivalent of 9^9 x 9^-6 is 729.
To find the numerical equivalent of 9^9 x 9^-6, we can simplify the expression one step at a time.
First, let's simplify the exponents:
9^9 can be written as 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 = 387,420,489.
9^-6 can be written as 1/9^6. To simplify this, we raise 9 to the power of 6:
1/9^6 = 1/(9 x 9 x 9 x 9 x 9 x 9) = 1/531,441.
Now, we can multiply these two values together:
387,420,489 x (1/531,441) = 0.729.
Therefore, the numerical equivalent of 9^9 x 9^-6 is 0.729.