Question

(2/3)^5 divided by (2/3)^4 divided by (2/3)^3​

Answer 1

Answer:

Result:

(2/3)^5 : (2/3)^4 : (2/3)^3 = 9/

4

= 2 1/

4

= 2.25

Spelled result in words is nine quarters (or two and one quarter).

How do you solve fractions step by step?

Exponentiation: 2/

3

^ 5 = 25/

35

= 32/

243

In words - two thirds raised to the power of to five = thirty-two two-hundred forty-thirds.

Exponentiation: 2/

3

^ 4 = 24/

34

= 16/

81

In words - two thirds raised to the power of to four = sixteen eighty-firsts.

Divide: the result of step No. 1 : the result of step No. 2 = 32/

243

: 16/

81

= 32/

243

· 81/

16

= 32 · 81/

243 · 16

= 2592/

3888

= 1296 · 2/

1296 · 3

= 2/

3

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 16/

81

is 81/

16

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 1296 gives 2/

3

.

In words - thirty-two two-hundred forty-thirds divided by sixteen eighty-firsts = two thirds.

Exponentiation: 2/

3

^ 3 = 23/

33

= 8/

27

In words - two thirds raised to the power of cubed = eight twenty-sevenths.

Divide: the result of step No. 3 : the result of step No. 4 = 2/

3

: 8/

27

= 2/

3

· 27/

8

= 2 · 27/

3 · 8

= 54/

24

= 6 · 9/

6 · 4

= 9/

4

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 8/

27

is 27/

8

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 6 gives 9/

4

.

In words - two thirds divided by eight twenty-sevenths = nine quarters.

Answer 2

Alright, we know that $a^m$÷$a^n = a^{m-n}$

Our question is:

$\frac{2}{3}^{5}$÷ $\frac{2}{3}^4$÷ $\frac{2}{3}^3$

So,

$\frac{2}{3}^{5-4}$ ÷ $\frac{2}{3}^3$

$\frac{2}{3}^1$÷ $\frac{2}{3}^3$

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

$\frac{2}{3}^{-2}$

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

= $\frac{9}{4}$

= $2 \frac{1}{4}$ or $2.25$

Hope this Helped!

Stay safe, stay sanitized and stay blessed!

ヾ(•ω•`)o