Question

Express $(\frac{1}{\sqrt{3} } )^{7}$ in the form $\frac{1}{b\sqrt{3} }$ where b is an integer:
Express $(\frac{1}{\sqrt{3} } )^{7}$ in the form $\frac{\sqrt{3} }{c}$ where c is an integer:
I will award Brainiest to the person with the correct answer and a good explanation! I NEED an explanation. Thanks! Please help!

Answer 1

Answer:

Express $(\frac{1}{\sqrt{3} } )^{7}$ in the form $\frac{1}{b\sqrt{3} }$ where b is an integer:

Express $(\frac{1}{\sqrt{3} } )^{7}$ in the form $\frac{\sqrt{3} }{c}$ where c is an integer:

I will award Brainiest to the person with the correct answer and a good explanation! I NEED an explanation. Thanks!

Answer 2

Answer:

b = 27, c = 81

Explanation:

b) (i) Given:

$\left(\dfrac{1}{\sqrt{3} } \right)^7$

expand:

$\left(\dfrac{1}{\sqrt{3} } \right)\left(\dfrac{1}{\sqrt{3} } \right)\left(\dfrac{1}{\sqrt{3} } \right)\left(\dfrac{1}{\sqrt{3} } \right)\left(\dfrac{1}{\sqrt{3} } \right)\left(\dfrac{1}{\sqrt{3} } \right)\left(\dfrac{1}{\sqrt{3} } \right)$

multiply pairs of expression, simplifying to:

$\left(\dfrac{1}{3} \right)\left(\dfrac{1}{3} \right)\left(\dfrac{1}{3} \right)\left(\dfrac{1}{\sqrt{3} } \right)$

multiply common integers:

$\left(\dfrac{1}{27} \right)\left(\dfrac{1}{\sqrt{3} } \right)$

evaluate following:

$\dfrac{1}{27\sqrt{3} } \right$

Hence, the value of b is 27.

(ii) Rationalizing expression:

$\dfrac{1}{27\sqrt{3} } \right$

multiply both numerator and denominator by root 3

$\dfrac{1}{27\sqrt{3} } \right \times\dfrac{\sqrt{3}}{\sqrt{3}}$

evaluate

$\dfrac{\sqrt{3}}{27(3)}$

multiply

$\dfrac{\sqrt{3}}{81}$

Hence, the value of c is 81.