Q:

Does anyone know how to do this and if so can you please help me and explain how to do it, it’ll be appreciated thank you

Accepted Solution

A:
Answer:13) [tex](5x)^{-\frac{5}{4}[/tex] ⇒ [tex]\frac{1}{\sqrt[4]{(5x)^5}}[/tex] 15) [tex](10n)^{\frac{3}{2}[/tex] ⇒ [tex]\sqrt{(10n)^3}[/tex] Step-by-step explanation:Given expression:13) [tex](5x)^{-\frac{5}{4}[/tex]15) [tex](10n)^{\frac{3}{2}[/tex]Write the expressions in radical form.Solution:For an expression with exponents as fraction like [tex](x)^{\frac{m}{n}[/tex]the numerator [tex]m[/tex] represents the power it is raised to and the denominator [tex]n[/tex] represents the nth root of the expression.For an expression with exponents as negative  fraction like [tex](x)^{-\frac{m}{n}[/tex]We take the reciprocal of the term by rule for negative exponents.So it is written as:[tex]\frac{1}{(x)^{\frac{m}{n}}}[/tex]using the above properties we can write the given expressions in radical form.13) [tex](5x)^{-\frac{5}{4}[/tex]⇒ [tex]\frac{1}{(5x)^{\frac{5}{4}}}[/tex]   [Using rule of negative exponents]⇒ [tex]\frac{1}{\sqrt[4]{(5x)^5}}[/tex]    [writing in radical form]15) [tex](10n)^{\frac{3}{2}[/tex]⇒ [tex]\sqrt{(10n)^3}[/tex]     [Since 2nd root is given as [tex]\sqrt{}[/tex] in radical form]