Betty has worked out the financing of her coffee shop. She plans to use the money in a savings account for her start-up costs. The savings account was opened by her grandmother five years ago. To figure out the annual interest rate, Betty needs to evaluate the expression fifth root of x • 10^4 end root. Betty wants to simplify this expression in terms of fractional exponents, and write it in the form x^a • 10^b
What is the value of a, the power of x?
What is the value of b, the power of 10?
To simplify the expression in terms of fractional exponents, we need to express the fifth root of x • 10^4 as x^a • 10^b.
Let's start with the fifth root of x:
(x)^(1/5)
Next, let's express 10^4 as (10^4)^(1).
(x)^(1/5) • (10^4)^(1)
To simplify further, we can apply the property of exponents that says (a^m)^n = a^(m*n):
(x)^(1/5) • (10^(4*1))
Simplifying the expression gives us:
x^(1/5) • 10^4
Therefore, the value of a, the power of x, is 1/5, and the value of b, the power of 10, is 4.
To simplify the expression in terms of fractional exponents, you need to rewrite the expression using fractional exponents instead of the radical sign.
The expression given is the fifth root of x • 10^4.
You can rewrite the fifth root of x as x^(1/5). This is because raising a number to the power of 1/n is equivalent to taking the nth root of the number.
So the expression can be rewritten as x^(1/5) • 10^4.
Now, since the expression is in the form x^a • 10^b, we can determine the values of a and b.
In this case, a is the power of x, which is 1/5, and b is the power of 10, which is 4.
Therefore, the value of a, the power of x, is 1/5, and the value of b, the power of 10, is 4.