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. ﻿−m2y5-m \sqrt{$$2y^5$$}
−m2y5​

Accepted Answer

Identify the given expression and determine whether it is in exponential or radical form. The expression is $$-m \sqrt{2y^{5}}$$, which is in radical form because it contains a square root symbol ($$\sqrt{\cdot}). $$Recall the relationship between radicals and exponents: $$\sqrt[n]{a} = a^{\frac{1}{n}}. $$For a square root, $$n = 2$$, so $$\sqrt{a} = a^{\frac{1}{2}}. $$Rewrite the radical expression $$\sqrt{2y^{5}}$$ using exponents: $$\sqrt{2y^{5}} = (2y^{5})^{\frac{1}{2}}. $$Apply the exponent to each factor inside the parentheses separately, using the property $$(ab)^c = a^c b^c. $$This gives $$2^{\frac{1}{2}} \cdot (y^{5})^{\frac{1}{2}}. $$Simplify the exponent on $$y by $$multiplying the exponents: $$y^{5 \cdot \frac{1}{2}} = y^{\frac{5}{2}}. So $$the expression in exponential form is $$-m \cdot 2^{\frac{1}{2}} \cdot y^{\frac{5}{2}}.$$

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. $-m \(\sqrt{2y^5}\)$

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Key Concepts

Exponential and Radical Forms

Properties of Exponents

Evaluating Expressions with Positive Variables

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. −m2y5-m \(\sqrt{2y^5}\)−m2y5