Question

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

Answer 1

Answer:

13) $(5x)^{-\frac{5}{4}$ ⇒ $\frac{1}{\sqrt[4]{(5x)^5}}$

15) $(10n)^{\frac{3}{2}$ ⇒ $\sqrt{(10n)^3}$

Step-by-step explanation:

Given expression:

13) $(5x)^{-\frac{5}{4}$

15) $(10n)^{\frac{3}{2}$

Write the expressions in radical form.

Solution:

For an expression with exponents as fraction like

$(x)^{\frac{m}{n}$

the numerator $m$ represents the power it is raised to and the denominator $n$ represents the nth root of the expression.

For an expression with exponents as negative  fraction like

$(x)^{-\frac{m}{n}$

We take the reciprocal of the term by rule for negative exponents.

So it is written as:

$\frac{1}{(x)^{\frac{m}{n}}}$

using the above properties we can write the given expressions in radical form.

13) $(5x)^{-\frac{5}{4}$

⇒ $\frac{1}{(5x)^{\frac{5}{4}}}$   [Using rule of negative exponents]

⇒ $\frac{1}{\sqrt[4]{(5x)^5}}$    [writing in radical form]

15) $(10n)^{\frac{3}{2}$

⇒ $\sqrt{(10n)^3}$     [Since 2nd root is given as $\sqrt{}$ in radical form]