Question

Simplify (1/216)^-2/3÷(1/27)^-4/3

Answer 1

(1): "^-4" was replaced by "^(-4)". 1 more similar replacement(s)

Step by step solution :

Step  1  :

1 Simplify —— 27

Equation at the end of step  1  :

(1 (1 {————+——— 2163 273

Step  2  :

 2.1     27 = 33 (27)-4 = (33)(-4) = (3)(-12)

Equation at the end of step  2  :

1 1 {———}-2 ÷ 3 + ———————— ÷ 3 216 (3)(-12)

Step  3  :

1 Divide ———————— by 3 (3)(-12)

Raising to a Power :

 3.1    312   divided by   31   = 3(12 - 1) = 311

Equation at the end of step  3  :

(1 {———}-2 ÷ 3 + 311 216

Step  4  :

1 Simplify ——— 216

Equation at the end of step  4  :

(1 (———)-2) ÷ 3 + 311 216

Step  5  :

 5.1     216 = 23•33 (216)-2 = (23•33)(-2) = (2)(-6) • (3)(-6)

Equation at the end of step  5  :

1 ————————————————— ÷ 3 + 311 ((2)(-6)•(3)(-6))

Step  6  :

1 Divide ————————————————— by 3 ((2)(-6)•(3)(-6))

Dividing exponents :

 6.1    36   divided by   31   = 3(6 - 1) = 35

Equation at the end of step  6  :

(26•35) + 311

Step  7  :

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{Given fractional expression,}$

$\sf{ \bigg( \frac{1}{216} \bigg) ^{ - \frac{2}{3} } \div \bigg( \frac{1}{27} \bigg)^{ - \frac{4}{3} } }$

$\sf{ \Rightarrow \: (216 {)}^{ \frac{2}{3} } \div (27 {)}^{ \frac{4}{3} } }$

$\sf{ \Rightarrow \: ( {6}^{3} {)}^{ \frac{2}{3} } \div ( {3}^{3} {)}^{ \frac{4}{3} } }$

$\sf{ \Rightarrow \: {6}^{ \cancel3 \times \frac{2}{ \cancel3} } \div {3}^{ \cancel3 \times \frac{4}{ \cancel3} } }$

$\sf{ \Rightarrow \: {6}^{2} \div {3}^{4} }$

$\sf{ \Rightarrow \: 6 \times 6 \div 3 \times 3 \times 3 \times 3}$

$\sf{ \Rightarrow \: 36 \div 81}$

$\sf{ \Rightarrow \: \frac{36}{81} }$