Write with fractional exponents. [tex]$\sqrt[3]{y^2}$[/tex]
Answer (2)
The expression 3 y 2 can be rewritten with fractional exponents as y 3 2 . This conversion follows the rule that states n x m = x n m . Therefore, the final answer is y 3 2 .
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y 3 2
Explanation
Understanding the Problem We are asked to rewrite the expression 3 y 2 using fractional exponents. This involves understanding the relationship between radicals and fractional exponents.
Recalling the Rule Recall that a radical expression of the form n x m can be written using fractional exponents as x n m . In this case, we have n = 3 and m = 2 .
Applying the Rule to the Expression Applying this rule to the given expression, we get 3 y 2 = y 3 2 .
Final Answer Therefore, the expression 3 y 2 written with fractional exponents is y 3 2 .
Examples
Fractional exponents are useful in various fields, such as physics and engineering, when dealing with equations involving roots and powers. For example, when calculating the period of a pendulum, you might encounter expressions with square roots. Rewriting these using fractional exponents can simplify the calculations and make it easier to manipulate the equations. Understanding fractional exponents allows for easier manipulation and simplification of complex equations in various scientific and engineering applications.
