How do you evaluate and simplify $\frac{11^{\frac{2}{5}}}{11^{\frac{4}{5}}}$ $11^(2/5)/11^(4/5)$ ?

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How do you evaluate and simplify $\frac{11^{\frac{2}{5}}}{11^{\frac{4}{5}}}$ $11^(2/5)/11^(4/5)$ ?

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Answer 1 · 2016-09-01T14:58:20

$\frac{1}{\sqrt[5]{11^{2}}}$ $1/(root5(11^2))$

To evaluate, use a calculator to get $0.3832 .$ $0.3832.$

Explanation:

When we are working with indices, the bases can be numbers or variables - the laws stay the same.

In this case both bases are 11.

Use the law of indices for dividing.

"If the bases are the same and you are dividing, subtract the indices"

$\frac{x^{m}}{x^{n}} = x^{m - n}$ $x^m/x^n = x^(m-n)$

$\frac{11^{\frac{2}{5}}}{11^{\frac{4}{5}}} \leftarrow$ $11^(2/5)/11^(4/5) larr$ the bottom index is bigger.

$\frac{1}{11^{\frac{4}{5} - \frac{2}{5}}} = \frac{1}{11^{\frac{2}{5}}} \leftarrow$ $1/11^(4/5 -2/5) = 1/(11^(2/5)) larr$ answers should have positive indices.

An index that is a fraction is a combination of a power and a root.

$x^{\frac{p}{q}} = \sqrt[q]{x^{p}}$ $x^(p/q) = rootq(x^p)$

$\frac{1}{11^{\frac{2}{5}}} = \frac{1}{\sqrt[5]{11^{2}}}$ $1/(11^(2/5)) = 1/(root5(11^2))$

To evaluate, use a calculator to get $0.3832 .$ $0.3832.$

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How do you evaluate and simplify $\frac{11^{\frac{2}{5}}}{11^{\frac{4}{5}}}$ $11^(2/5)/11^(4/5)$ ?

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How do you evaluate and simplify $\frac{11^{\frac{2}{5}}}{11^{\frac{4}{5}}}$ $11^(2/5)/11^(4/5)$ ?