Question

last problem, Pls HELP !!

http://prntscr.com/1rzdtm

Answer 1

Problem 3 :-


\(\huge \frac{x^\frac{2}{3}}{x^\frac{4}{9}}\)

Using Quotient of a Power Property,
\(\large \color{red}{\frac{a^m}{a^n} = a^{m-n}}\)

\(\huge x^{\frac{2}{3}-\frac{4}{9}}\)

\(\huge x^{\frac{2\times 3}{3\times 3}-\frac{4}{9}}\)

\(\huge x^{\frac{6}{9}-\frac{4}{9}}\)

\(\huge x^{\frac{2}{9}}\)

\(\color{red}{\text{rational exponent can be written as radical}} \)

\(\huge \sqrt[9]{x^2}\)

Answer 2

@Nurialozza96

Answer 3

Problem 4 :-
** \(\huge \sqrt[3]{x^3}\)

radical can be written in exponent form as

\(\huge (x^{3})^{\frac{1}{3}}\)

using Power of a Power property,
\(\large \color{red}{(a^m)^n = a^{mn}}\)

\(\huge x^{3 \times \frac{1}{3}}\)

\(\huge x\)

============

** \(\huge x^{\frac{1}{3}}.x^{\frac{1}{3}}.x^{\frac{1}{3}}\)

using Product of a Power property,
\(\large \color{red}{a^m . a^n = a^{m+n}}\)

\(\huge x^{\frac{1}{3}+\frac{1}{3} + \frac{1}{3}}\)

\(\huge x^{\frac{3}{3}}\)

\(\huge x\)

==========

** \(\huge \frac{1}{x^{-1}}\)

According to the definition of negative exponent,


\(\huge \frac{1}{\frac{1}{x}}\)

\(\huge x\)

================

** \(\huge \sqrt[11]{x^5.x^4.x^2}\)

using Product of a Power property,
\(\large \color{red}{a^m . a^n = a^{m+n}}\)

\(\huge \sqrt[11]{x^{5+4+2}}\)

\(\huge \sqrt[11]{x^{11}}\)

radical can be written as exponent,

\(\huge (x^{11})^{\frac{1}{11}}\)

using Power of a Power property,
\(\large \color{red}{(a^m)^n = a^{mn}}\)

\(\huge x^{11 \times \frac{1}{11}}\)

\(\huge x\)

Answer 4

oh this is gonna take a while to write down xD