Question

question 12
write each expression in exponential form.
i. \\(\frac{9}{\sqrt4{13}}\\)
ii. \\(\sqrt5{y + 10z}\\)
iii. \\(-\frac{2}{\sqrt7{11x + 5y}}\\)
question 13
simplify the expression. assume all variables are positive. make sure to answer with a rationalized denominator.
\\(\sqrt{\frac{100x^3}{81x}} = \\)

Explanation:

Step1: Convert root to exponent (I)

$\frac{9}{13^{\frac{1}{4}}} = 9 \cdot 13^{-\frac{1}{4}}$

Step2: Convert root to exponent (II)

$\sqrt[6]{y+10x} = (y+10x)^{\frac{1}{6}}$

Step3: Convert root to exponent (III)

$-\frac{2}{\sqrt[7]{11x+5y}} = -2 \cdot (11x+5y)^{-\frac{1}{7}}$

Step4: Simplify radicand (Q13)

$\sqrt{\frac{100x^3}{81x}} = \sqrt{\frac{100x^2}{81}}$

Step5: Split root into parts (Q13)

$\sqrt{\frac{100x^2}{81}} = \frac{\sqrt{100x^2}}{\sqrt{81}}$

Step6: Evaluate roots (Q13)

$\frac{\sqrt{100x^2}}{\sqrt{81}} = \frac{10x}{9}$

Answer:

I. $9 \cdot 13^{-\frac{1}{4}}$
II. $(y+10x)^{\frac{1}{6}}$
III. $-2 \cdot (11x+5y)^{-\frac{1}{7}}$
Question 13: $\frac{10x}{9}$