Question

Evaluate the left hand side to find the value of a in the equation in simplest form. (x^((1)/(5)))^((5)/(4))=x^(a)

Answer 1

To find the value of 'a', the exponent rules are applied to the expression (x^(1/5))^(5/4), which simplifies to x when you multiply the exponents (1/5)*(5/4), resulting in the value of 'a' being 1.

Step-by-step explanation:

To evaluate the left-hand side of the given equation (x^((1)/(5)))^((5)/(4))=x^(a) and find the value of 'a' in simplest form, we will first look at how exponents can be combined. In mathematics, when you raise a power to another power, you multiply the exponents. Following this rule, we can simplify the expression on the left-hand side.

Here's how it works:

1. Take the expression (x^(1/5)) which means the fifth root of 'x'.
2. Now, raise it to the power of 5/4: ((x^(1/5))^(5/4)).
3. According to the laws of exponents, when you raise a power to another power, you multiply the exponents: (1/5) times (5/4) equals 1.
4. Therefore, the expression simplifies to x^(1), which is just 'x'.

Putting it all together:

(x^(1/5))^(5/4) = x^((1/5)*(5/4)) = x^1 = x

So, the value of 'a' in the equation x^(a) is 1.