Question

Find the value of (8/27)⅓

Answer 1

Answer:

$\frac{2}{3} =0.6$ or $\frac{8}{27}$×$\frac{1}{3}=$$\frac{8}{81}$

Step-by-step explanation:

$(\frac{8}{27} )^\frac{1}{3} \\=\frac{8^\frac{1}{3} }{27^\frac{1}{3} }$

simplify the numerator

rewrite 8 as 2³

$=(\frac{(2^3)^\frac{1}{3} }{27^\frac{1}{3} }$

apply the power rule

∴$(a^m)^n=a^m^n$

so ,  

$=\frac{2^3^(\frac{^1}{^3})}{27^\frac{1}{3} }$

cancel the common factor 3 i.e 3×1/3=1

$=\frac{2^1}{27^\frac{1}{3} }$

evaluate the exponent

$=\frac{2}{27^\frac{1}{3} }$

simplify the denominator

apply the power rule

∴$(a^m)^n=a^m^n$

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

therefore , 3×1/3=1

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

$=\frac{2}{3}$

=0.6