Question

If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. -5z2/3

Accepted Answer

Identify the given expression: $$-5z^{2/3}. $$Notice that the exponent $$2/3 is a $$fractional exponent, which means the expression is currently in exponential form. Recall the rule for converting from exponential form to radical form: $$a^{m/n}$$ = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$$. Here, the denominator of the exponent (3) is the root, and the numerator (2) is the power. Rewrite z$$^{2/3}$$ in radical form as $$\left(\sqrt[3]{z}\$$right)^2 or $$equivalently $$\sqrt[3]{z^2$}. So $$the entire expression becomes $$-5 \left(\sqrt[3]{z}\$$right)^2$$ or -5$$ \sqrt[3]{$$z^2$$}$$. Since the problem states to evaluate if possible, and variables represent positive real numbers, you can leave the expression in radical form as is because it cannot be simplified further without knowing the value of z$. If you were to convert back to exponential form from the radical form -5$$ \sqrt[3]{$$z^2$$}$$, you would write it as -5$$ $$z^{2/3}$$, confirming the equivalence of the two forms.

If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. -5z^2/3

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Key Concepts

Exponential and Radical Forms

Fractional Exponents

Evaluating Expressions with Positive Real Variables