Question

[2/3]² ÷ [4/5]³ × [3/5]² evaluate the expression ​(sum from exponent chapter) (follow the exponent laws and then answer) (i need the answer step by step) (the final answer is 5[1/2]⁴) ​

Answer 1

Answer:

[2/3]² ÷ [4/5]³ × [3/5]² = 5[1/2]⁴

Step-by-step explanation:

[2/3]² ÷ [4/5]³ × [3/5]² = (2/3*2/3) ÷ (4/5×4/5×4/5) × (3/5×3/5) = 4/9 ÷ 64/125 × 9/25=5/16

5[1/2]⁴=

[1/2]⁴=1/2*1/2*1/2*1/2=1/16

5*1/16=5/16

5[1/2]⁴=5/16

Answer 2

Given data: $(\frac{2}{3})^2$÷ $(\frac{4}{5})^3$× $(\frac{3}{5})^2$

To find: Simplify the given equation

Solution:

According to the mathematic rule division will be done first and next will be multiplication.

$(\frac{2}{3} X \frac{2}{3} )$ ÷ $(\frac{4}{5} X \frac{4}{5} X \frac{4}{5} )$ × $(\frac{3}{5} X \frac{3}{5} ) =$ $\frac{4}{9}$ ÷ $\frac{64}{125}$ × $\frac{9}{25}$

Dividing the first 2 fraction we get,

$\frac{4}{9}$ × $\frac{125}{64} = \frac{1}{9}$ × $\frac{125}{16}$

Multiplying the 3 fractions $\frac{1}{9}$ × $\frac{125}{16}$ × $\frac{9}{25} =\frac{5}{16}$.

Hence the simplification of given number is $\frac{5}{16}$ or $5(\frac{1}{2} )^4$ ( $2^4=16$).