Which expression is equivalent to x^-5/3

We are asked to find an expression that is equivalent to the expression [tex]x^{-\frac{5}{3}}[/tex]. Since we have a negative exponent, we can make it a positive one by putting the whole expression under 1. This gives us [tex]\frac{1}{x^{\frac{5}{3}}}[/tex]. Notice that the negative sign is gone from the exponent. Now, we can convert the fractional exponent to radical form. We can do this by following -
[tex]x^ \frac{a}{b} = \sqrt[b]{x^a} [/tex]. Here, we get that [tex]a=5,b=3[/tex]. So, when we convert the expression to radical form using the formula we got, we get [tex]\boxed{\frac{1}{\sqrt[3]{x^5}}}[/tex], which is our answer. Hope this helped!

codiepienagoya codiepienagoya · Answer 2 · 2022-01-25T10:28:54+01:00

The answer is "[tex]\bold{\frac{1}{\sqrt[3]{x^5}}} [/tex]", and the further calculation to the given expression can be defined as follows:

Given:

[tex] \to x^{-\frac{5}{3}} [/tex]

To find:

solve expression=?

Solution:

[tex]\to x^{-\frac{5}{3}}= \frac{1}{x^{\frac{5}{3}}} [/tex]

[tex]= \frac{1}{\sqrt[3]{x^5}} [/tex]

So, the final answer is "Option b".

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