Question

convert each power to radical notation.
i. $3^{\frac{1}{4}}$
ii. $10^{-\frac{1}{4}}$
question 12
write each expression in exponential form.
i. $\frac{9}{\sqrt4{13}}$
ii. $\sqrt6{y + 10x}$
iii. $-\frac{2}{\sqrt7{11x + 5y}}$

Explanation:

Step1: Convert $3^\frac{1}{4}$ to radical

Recall $a^\frac{1}{n}=\sqrt[n]{a}$. So $3^\frac{1}{4}=\sqrt[4]{3}$

Step2: Convert $10^{-\frac{1}{3}}$ to radical

Use $a^{-\frac{1}{n}}=\frac{1}{\sqrt[n]{a}}$. So $10^{-\frac{1}{3}}=\frac{1}{\sqrt[3]{10}}$

Step3: Convert $\frac{9}{\sqrt[4]{13}}$ to exponential

Rewrite radical as exponent: $\sqrt[4]{13}=13^\frac{1}{4}$, so $\frac{9}{\sqrt[4]{13}}=9\times13^{-\frac{1}{4}}$

Step4: Convert $\sqrt[6]{y+10x}$ to exponential

Recall $\sqrt[n]{a}=a^\frac{1}{n}$. So $\sqrt[6]{y+10x}=(y+10x)^\frac{1}{6}$

Step5: Convert $-\frac{2}{\sqrt[7]{11x+5y}}$ to exponential

Rewrite radical as exponent: $\sqrt[7]{11x+5y}=(11x+5y)^\frac{1}{7}$, so $-\frac{2}{\sqrt[7]{11x+5y}}=-2\times(11x+5y)^{-\frac{1}{7}}$

Answer:

Radical Notation:

I. $\sqrt[4]{3}$
II. $\frac{1}{\sqrt[3]{10}}$

Exponential Form:

I. $9\times13^{-\frac{1}{4}}$
II. $(y+10x)^\frac{1}{6}$
III. $-2\times(11x+5y)^{-\frac{1}{7}}$