Simplified form of left[left(sqrt[5]{x^{-3 / | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given expression: $\left[\left(\sqrt[5]{x^{-3 / 5}}\right)^{-5 / 3}\right]^{5}$Using the property $\sqrt[n]{a} = a^{1/n}$,we can write $\sqrt[5]{x

Vedclass · Accepted Answer

$x$

Vedclass · Answer

(C) Given expression: $\left[\left(\sqrt[5]{x^{-3 / 5}}ight)^{-5 / 3}ight]^{5}$Using the property $\sqrt[n]{a} = a^{1/n}$,we can write $\sqrt[5]{x^{-3/5}} = (x^{-3/5})^{1/5} = x^{-3/25}$.Now,applying the power rule $(a^m)^n = a^{m 	imes n}$ repeatedly:$= \left( (x^{-3/5})^{1/5} ight)^{-5/3 	imes 5}$$= (x^{-3/5})^{1/5 	imes -5/3 	imes 5}$$= (x^{-3/5})^{-25/15}$$= (x^{-3/5})^{-5/3}$$= x^{(-3/5) 	imes (-5/3)}$$= x^{1} = x$.

Simplified form of $\left[\left(\sqrt[5]{x^{-3 / 5}}\right)^{-5 / 3}\right]^{5}$ is

Similar Questions

What is the simplified value of $(x^{128}+1)(x^{64}+1)(x^{32}+1)(x^{16}+1)(x^{8}+1)(x^{4}+1)(x^{2}+1)(x+1)$?

The difference between the sum of $1 \frac{3}{4}, 2 \frac{1}{3}, 3 \frac{5}{12}, 5 \frac{1}{5}$ and $2 \frac{1}{6}$ and the nearest whole number is

Choose the incorrect relation$(s)$ from the following:
$(i)$ $\sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3}$
$(ii)$ $\sqrt{6}+\sqrt{2}<\sqrt{5}+\sqrt{3}$
$(iii)$ $\sqrt{6}+\sqrt{2}>\sqrt{5}+\sqrt{3}$

$\frac{\frac{1}{3}+\frac{1}{3} \times \frac{1}{3}}{\frac{1}{3}+\frac{1}{3} \text{ of } \frac{1}{3}}-\frac{1}{9} = ?$

What is the value of $9 \frac{1}{3} + 19 \frac{2}{3} + 20 \frac{3}{4} + 19 \frac{1}{4}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module