What is the missing number in the simplified exponent expression of 5 ^ 5 ^ 7 = 5 ^ 9
The missing number in the simplified expression is 7.
To find the missing number in the simplified exponent expression of 5 ^ 5 ^ 7 = 5 ^ 9, we need to understand the laws of exponents.
In this equation, we have the expression 5 raised to the power of 5 raised to the power of 7, which is then equal to 5 raised to the power of 9.
According to the laws of exponents, when a number is raised to a power and then that result is raised to another power, we multiply the exponents.
So, to simplify this equation, we need to multiply the exponents:
7 * 5 = 35
Therefore, the missing number is 35.
To find the missing number in the simplified exponent expression, we can consider the basic rules of exponents.
In the given expression, 5 ^ 5 ^ 7 = 5 ^ 9, the outer exponent is 7, which is the exponent of the exponent or the power tower.
To simplify this expression, we need to calculate 5 raised to the power of 5, which gives us 5^5 = 3125.
Now, we can substitute this value back into the original expression to get: 5 ^ 3125 ^ 7 = 5 ^ 9.
Now, since the exponent of the exponent is 7, we need to calculate 3125 raised to the power of 7, which is (3125^7).
To calculate this, we can use a calculator or a programming language that supports large number calculations. Evaluating this expression gives us a very large number.
Therefore, the missing number in the simplified exponent expression is the result of raising 3125 to the power of 7.