To write:

The radical expression using exponent$y}^{-\frac{5}{3}$

The radical expression using exponent

Ernstfalld
2020-11-08
Answered

To write:

The radical expression using exponent$y}^{-\frac{5}{3}$

The radical expression using exponent

You can still ask an expert for help

estenutC

Answered 2020-11-09
Author has **81** answers

Step 1

Definition used:

For any rational exponent$\frac{m}{n}$ in lowest terms, where m and n are integers and $n>0,$ we define

$a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m$ or equivalently $a}^{\frac{m}{n}}=\sqrt{n}\left\{{a}^{m}\right\$

If n is even, then we require that$a\ge 0.$

Step 2

Consider,$y}^{-\frac{5}{3}$

From the above definition$a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m$ the exponent notation of $y}^{-\frac{5}{3}$ is written as,

$y}^{-\frac{5}{3}}=\frac{1}{{y}^{\frac{5}{3}}$

$=\frac{1}{{\left({y}^{5}\right)}^{\frac{1}{3}}}$

$y}^{-\frac{5}{3}}=\frac{1}{\sqrt{3}\left\{{y}^{5}\right\}$

Therefore radical notation of the radical$y}^{-\frac{5}{3}$ is $\frac{1}{\sqrt{3}\left\{{y}^{5}\right\}}$

Definition used:

For any rational exponent

If n is even, then we require that

Step 2

Consider,

From the above definition

Therefore radical notation of the radical

asked 2022-04-20

Solving

${\mathrm{log}}_{2}(x-4)+{\mathrm{log}}_{2}(x+2)=4$

Here is how I have worked it out so far:

${\mathrm{log}}_{2}(x-4)+\mathrm{log}(x+2)=4$

${\mathrm{log}}_{2}\left((x-4)(x+2)\right)=4$

$(x-4)(x+2)={2}^{4}$

$(x-4)(x+2)=16$

How do I proceed from here?

${x}^{2}+2x-8=16$

${x}^{2}+2x=24$

$x(x+2)=24$ Which I know is not the right answer

${x}^{2}+2x-24=0$ Can't factor this

Here is how I have worked it out so far:

How do I proceed from here?

asked 2021-01-08

Radicals and Exponents Evaluate each expression:

a)$\frac{\sqrt{132}}{\sqrt{3}}$

b)$\sqrt{3}\left\{2\right\}\sqrt{3}\left\{32\right\}$

c)$\sqrt{4}\left\{\frac{1}{4}\right\}\sqrt{4}\left\{\frac{1}{64}\right\}$

a)

b)

c)

asked 2022-01-31

How do you write $y=\frac{7}{2}x$ in standard form?

asked 2022-07-22

If $2\cdot lo{g}_{e}(x-2y)=lo{g}_{e}y+lo{g}_{e}x$, then find the numerical value of $\frac{x}{y}$

My try:

$2\cdot lo{g}_{e}(x-2y)=lo{g}_{e}y+lo{g}_{e}x$

$lo{g}_{e}(x-2y{)}^{2}=lo{g}_{e}xy$

$(x-2y{)}^{2}=xy$

But expanding the LHS doesn't give the result. What should I do further?

My try:

$2\cdot lo{g}_{e}(x-2y)=lo{g}_{e}y+lo{g}_{e}x$

$lo{g}_{e}(x-2y{)}^{2}=lo{g}_{e}xy$

$(x-2y{)}^{2}=xy$

But expanding the LHS doesn't give the result. What should I do further?

asked 2021-12-07

Factor completely each polynomial, and indicate any that are not factorable using integers. $4{n}^{2}+25n+36$

asked 2022-01-21

Prove $\sum _{\{n=2\}}^{\mathrm{\infty}}\frac{1}{n\mathrm{ln}\left(n\right)\mathrm{ln}\mathrm{ln}n}$ is divergent.

asked 2022-08-08

(4x-3)squared=4 solve the equation

4x squared +12x=0

4x squared +12x=0