Question

Find the value of (1³+2³+3³)^-3/2​

Answer 1

Answer:

$\frac{1}{216}$

Step-by-step explanation:

Using the rule of exponents

$a^{-m}$ ⇔ $\frac{1}{a^{m} }$

$a^{\frac{m}{n} }$ = $\sqrt[n]{a^{m} }$

Evaluate the parenthesis

1³ + 2³ + 3³ = 1 + 8 + 27 = 36 , then

$(36)^{-\frac{3}{2} }$

= $\frac{1}{36^{\frac{2}{3} } }$

= $\frac{1}{(\sqrt{36})^3 }$

= $\frac{1}{6^{3} }$

= $\frac{1}{216}$