How do you write the expression ${(\sqrt{10})}^{3}$ $(sqrt10)^3$ in exponential form?

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Answer 1 · 2018-06-07T15:22:02

$10^{\frac{3}{2}}$ $10^(3/2)$

Definition for rational exponents:

$\sqrt[n]{a^{m}} = a^{\frac{m}{n}}$ $rootcolor(red)n(a^color(blue)m) = a^(color(blue)m/color(red)n)$

${(\sqrt{10})}^{3}$ $(sqrt(10))^3$

${(10^{\frac{1}{2}})}^{3}$ $(10^(1/2))^3$

now use rule:

${(a^{n})}^{m} = a^{m \cdot n}$ $(a^n)^m = a^(m*n)$

${(10^{\frac{1}{2}})}^{3} = 10^{\frac{3}{2}}$ $(10^(1/2))^3 = 10^(3/2)$

How do you write the expression (√10)3(sqrt10)^3 in exponential form?