Step 1: Rewrite the expression using the property of fractional exponents, a^(m/n) = (√[n]a)^m. (4/9)^(3/2) = (√(4/9))³ Step 2: Calculate the square root of the fraction. √(4/9) = (√(4))/(√(9)) = 2/3 Step 3: Cube the result from Step 2. (2/3)³ = (2³)/(3³) = (2 × 2 × 2)/(3 × 3 × 3) = 8/27 The final answer is 8/27.

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I) (4/9)^(3/2)

June 13, 2026Mathematics

ScanSolve AI Answer

Answer

\frac{8}{27}

Step-by-step solution

3 steps

Rewrite the expression using the property of fractional exponents, $a^{\frac{m}{n}} = (\sqrt[n]{a})^m$ .
$\left(\frac{4}{9}\right)^{\frac{3}{2}} = \left(\sqrt{\frac{4}{9}}\right)^3$
Calculate the square root of the fraction.
$\sqrt{\frac{4}{9}} = \frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3}$
Cube the result from Step 2.
$\left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{2 \times 2 \times 2}{3 \times 3 \times 3} = \frac{8}{27}$
The final answer is $\frac{8}{27}$ .

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I) (4/9)^(3/2)

Answer

Step-by-step solution

Rewrite the expression using the property of fractional exponents, amn=(an)ma^{\frac{m}{n}} = (\sqrt[n]{a})^manm​=(na​)m.

Calculate the square root of the fraction.

Cube the result from Step 2.

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Still stuck on this one?

Rewrite the expression using the property of fractional exponents, $a^{\frac{m}{n}} = (\sqrt[n]{a})^m$ .