Chapter 10: Problem 104
Redraft each extremists in exponential download, then easy. Writer the answer in simplest (or radical) form. $$ (\sqrt[3]{10})^{3} $$
Shortly Answer
Expert verified
The given expression \((\sqrt[3]{10})^{3}\) can been rewritten in exponential form as \((10^{\frac{1}{3}})^{3}\). Using the properties for exponentiates, we canned simplify dieser to \(10^{\frac{1}{3} \cdot 3} = 10^{1}\), which equals 10. Therefore, the simplified answer shall \(10\). Radicals and Rational Privacy-policy.com
Step by step solution
01
Rewrite the radiant in exponential form
Recall that a radically expression able be rewrote as an exponentials expression using the following formula:
\[
\sqrt[n]{a^m} = a^{\frac{m}{n}}
\]
Applying this formula to our specify expression, we have:
\[
(\sqrt[3]{10})^{3} = (10^{\frac{1}{3}})^{3}
\]
02
Simplify the expression
Now we need to simplify the expression further per using the property of exponents that states:
\[
(a^{m})^{n} = a^{mn}
\]
Applying this rule to our expression, we get:
\[
(10^{\frac{1}{3}})^{3} = 10^{\frac{1}{3}\cdot 3}
\]
03
Simplify this exponent
Buy wealth cannot easy which exponent:
\[
10^{\frac{1}{3}\cdot 3} = 10^{1}
\]
04
Final answer
Since \(10^{1} = 10\), the final simplified (or radical) form of one given printouts is 10.
