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# Rewrite without rational exponents, and simfly, if possible 256^{frac{3}{4}} # Rewrite without rational exponents, and simfly, if possible 256^{frac{3}{4}}

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Rational exponents and radicals asked 2021-02-09
Rewrite without rational exponents, and simfly, if possible $$\displaystyle{256}^{{{\frac{{{3}}}{{{4}}}}}}$$

## Answers (1) 2021-02-10
Step 1
Rational exponents (also called fractional exponents) are expressions with exponents that are rational numbers (as opposed to integers).
Given rational exponent is $$\displaystyle{256}^{{{\frac{{{3}}}{{{4}}}}}}$$, we have find answer without rational exponent.
Step 2
We know that
$$\displaystyle{256}={2}\ \times\ {2}\ \times\ {2}\ \times\ {2}\ \times\ {2}\ \times\ {2}\ \times\ {2}\ \times\ {2}$$
$$\displaystyle{256}={2}^{{{8}}}$$
We can write $$\displaystyle{256}^{{{\frac{{{3}}}{{{4}}}}}}$$ as
$$\displaystyle{256}^{{{\frac{{{3}}}{{{4}}}}}}={\left({2}^{{{8}}}\right)}^{{{\frac{{{3}}}{{{4}}}}}}={2}^{{{\frac{{{8}\ \times\ {3}}}{{{4}}}}}}$$
$$\displaystyle={2}^{{{2}\ \times\ {3}}}={2}^{{{6}}}$$
$$\displaystyle={2}\ \times\ {2}\ \times\ {2}\ \times\ {2}\ \times\ {2}\ \times\ {2}$$
$$\displaystyle={4}\ \times\ {4}\ \times\ {4}$$
$$\displaystyle{\left({256}\right)}^{{{\frac{{{3}}}{{{4}}}}}}={64}$$
So $$\displaystyle{256}^{{{\frac{{{3}}}{{{4}}}}}}={64}$$

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