Find the value of frac{8^{1/3} times 16^{1/3} | vedclass

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

Question

(B) To find the value of $\frac{8^{1/3} 	imes 16^{1/3}}{32^{-1/3}}$,we express each base as a power of $2$:$8 = 2^3$,$16 = 2^4$,and $32 = 2^5$.Substi

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(B) To find the value of $\frac{8^{1/3} 	imes 16^{1/3}}{32^{-1/3}}$,we express each base as a power of $2$:$8 = 2^3$,$16 = 2^4$,and $32 = 2^5$.Substituting these into the expression:$\frac{(2^3)^{1/3} 	imes (2^4)^{1/3}}{(2^5)^{-1/3}} = \frac{2^{3 	imes 1/3} 	imes 2^{4 	imes 1/3}}{2^{5 	imes -1/3}} = \frac{2^1 	imes 2^{4/3}}{2^{-5/3}}$.Using the laws of exponents $a^m 	imes a^n = a^{m+n}$ and $\frac{a^m}{a^n} = a^{m-n}$:$= 2^{1 + 4/3 - (-5/3)} = 2^{1 + 4/3 + 5/3} = 2^{1 + 9/3} = 2^{1 + 3} = 2^4$.$2^4 = 16$.

Find the value of $\frac{8^{1/3} \times 16^{1/3}}{32^{-1/3}}$.

Similar Questions

For each question,select the proper option from the four options given to make the statement true: $(\sqrt{5}+3)^{2}$ is a / an $\ldots \ldots \ldots$ number.

Arrange the following numbers in ascending order: $\sqrt{3}, \sqrt[3]{4}, \sqrt[4]{10}$

Find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.

$\sqrt[4]{\sqrt[3]{2^{2}}}$ equals

Which of the following is irrational?

Vedclass Test Series

Exam Paper Generator

Online Exam Module