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

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

Question
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 \(\displaystyle{256}^{{{\frac{{{3}}}{{{4}}}}}}={64}\)
0

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