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Describe how to transform the quantity of the sixth root of x to the fifth power, to the seventh power into an expression with a rational exponent. Make sure you respond with complete sentences.

Please answer the question the best way you can

Respuesta :

DeanR

Complete sentences?  Gimme a break.

I think this is describing

[tex](\sqrt[6]{x^5} )^7[/tex]

First step is we convert the sixth root to a 1/6 power,

[tex]=((x^5)^{\frac 1 6})^7[/tex]

In general when we have a power raised to a power we get to multiply the exponents,

[tex]=x^\frac{35}{6}[/tex]

That's our answer.

the sixth root of x to the fifth power, to the seventh power into an  rational exponent is [tex]x^\frac{35}{6}[/tex]

Given :

the quantity of the sixth root of x to the fifth power, to the seventh power

The given expression is [tex](\sqrt[6]{x^5} )^7[/tex]

To write it in rational exponent , we apply exponential property

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

The radical goes to the denominator of rational exponent

the exponent of x goes to the numerator of rational exponent .

lets write the radical part as rational exponent

[tex](\sqrt[6]{x^5} )^7\\(x^\frac{5}{6} )^7[/tex]

Now we multiply the exponents to make it as single exponent

[tex](x^\frac{5}{6} )^7\\\\x^\frac{35}{6}[/tex]

Learn more :

brainly.com/question/1503370