Show two steps to simplify each of the following expressions, and then calculate the value of each expression.
25 exponent 5/2
81 exponent 7/4
25^(5/2)
= (25^)1/2)^5
= 5^5
= 3125
you try the second, doing it the same way
To simplify the expressions and calculate their values, you can follow these two steps:
Step 1: Simplify the exponent expressions.
Step 2: Evaluate the simplified expressions.
Let's go through each expression:
Expression 1: 25^5/2
Step 1: Simplify the exponent expression.
To simplify the exponent expression 5/2, we need to apply the exponent rule for fractions. According to the rule, when a fraction is in the exponent, we can take the numerator (5) as the power of the base (25) and take the denominator (2) as the root.
So, 25^5/2 = (25^5)^(1/2)
Step 2: Evaluate the simplified expression.
Now we can calculate the value:
25^5 = 25 * 25 * 25 * 25 * 25 = 312,500
We then take the square root of the result:
√(312,500) ≈ 559.02
Therefore, 25^5/2 ≈ 559.02
Expression 2: 81^7/4
Step 1: Simplify the exponent expression.
Using the same exponent rule, we have:
81^7/4 = (81^7)^(1/4)
Step 2: Evaluate the simplified expression.
Now, let's calculate the value:
81^7 = 81 * 81 * 81 * 81 * 81 * 81 * 81 = 197,706,096,281
Then, we take the fourth root of the result:
∜(197,706,096,281) ≈ 2,379.68
Therefore, 81^7/4 ≈ 2,379.68
To summarize:
- 25^5/2 ≈ 559.02
- 81^7/4 ≈ 2,379.68