Sure, let's handle these expressions one by one.
### Part (b): Simplifying [tex]\((2 - x)^{\frac{1}{2}}\)[/tex]
The given expression is [tex]\((2 - x)^{\frac{1}{2}}\)[/tex].
1. Understanding the expression: The term [tex]\((2 - x)^{\frac{1}{2}}\)[/tex] is another way of writing the square root of [tex]\((2 - x)\)[/tex]. This is due to the property of exponents that [tex]\(a^{\frac{1}{2}}\)[/tex] means the square root of [tex]\(a\)[/tex].
2. Simplification: The expression doesn't actually require any further simplification if [tex]\(x\)[/tex] is unknown. Therefore, we can rewrite it as:
[tex]\[
(2 - x)^{\frac{1}{2}} = \sqrt{2 - x}
\][/tex]
So, [tex]\[ \boxed{\sqrt{2 - x}} \][/tex] is the simplified form of the expression [tex]\((2 - x)^{\frac{1}{2}}\)[/tex].
### Part (c): Evaluating [tex]\(\left(-\frac{3}{4}\right)^{\frac{3}{5}}\)[/tex]
The given expression is [tex]\(\left(-\frac{3}{4}\right)^{\frac{3}{5}}\)[/tex].
1. Understanding the expression: This expression raises a fraction [tex]\(\left(-\frac{3}{4}\right)\)[/tex] to the power of [tex]\(\frac{3}{5}\)[/tex].
2. Properties of exponents with negatives: It’s important to note that when a negative number is raised to a fractional exponent, it usually involves complex numbers unless the denominator of the fraction is even (which it is not, in this case).
3. Breaking it down:
[tex]\[
\left(-\frac{3}{4}\right)^{\frac{3}{5}}
\][/tex]
can be understood as finding the 5th root first and then cubing the result.
For simplicity here, we don’t perform these operations manually. Instead, we recognize that this computation generally results in a complex number. To be precise, the value [tex]\(\left(-\frac{3}{4}\right)^{\frac{3}{5}}\)[/tex] can be found using a calculator capable of handling complex numbers.
Without a calculator or computational tool, we leave it in its simplified form acknowledging its nature:
[tex]\[
\boxed{\left(-\frac{3}{4}\right)^{\frac{3}{5}}}
\][/tex]
The exact numerical value would typically be expressed in terms of complex numbers such as:
[tex]\[
\boxed{a + bi}
\][/tex]
where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] would be specific real numbers representing the real and imaginary parts.
Thus, [tex]\((2 - x)^{\frac{1}{2}} = \boxed{\sqrt{2 - x}}\)[/tex] and [tex]\(\left(-\frac{3}{4}\right)^{\frac{3}{5}} = \boxed{\left(-\frac{3}{4}\right)^{\frac{3}{5}}}\)[/tex].
