10 to power of minus a third x 25 to power of two thirds divided by 2 to power of five thirds?

Question

I suppose you do the division part first.

So you would do 25 to the power of two thirds and divide it by 2 to the power of five thirds and then you would multiply that answer by 10 to the power of minus a third.

This is all meant to be done without a calculator.  It sais to simplify!

Answer 1

me thank yu tri tu sae

(10^-1/3)*(25^2/3) / 2^5/3

10^-1/3=1/10^1/3=1/kube root (10)...kube root(10)=2.154434690031884

then 1/x giv 0.46415888336814703

25^2/3=kube root(25*25)=kube root(625)=8.549879733383484

1/2^5/3=2^-5/3...2^5=32, kube root=3.174802103936399, then 1/x giv 0.3149802624773295

Answer 2

To solve this problem, use rules for exponents such as shown below:

a^-n=1/a^n=(1/a)^n (a≠0), a^mn=(a^m)^n, and a^m/b^m=(a/b)^m (b≠0), where a,b,m,n are any real numbers with the limitations listed.   Each term of the given equations can be written as follows:

10 to the negative one-third: 10^(-1/3)=1/(10^(1/3))=(1/10)^(1/3), 25 to the two-thirds: 25^(2/3)=(25^2)^(1/3)=625^(1/3), and 2 to the five-thirds: 2^(5/3)=(2^5)^(1/3)=32^(1/3)

Thus, this problem can be solved as follows:

10^(-1/3) x 25^(2/3) ÷2^(5/3) = (1/10)^(1/3) x 625^(1/3) ÷ 32^(1/3)=(1/10 x 625 ÷ 32)^(1/3)

=(625/(10x32))^(1/3)=(125/64)^(1/3)=((5^3)/(4^3))^(1/3)=((5/4)^3)^(1/3)=(5/4)^(3x1/3)=5/4

Therefore, the answer is: 10^(-1/3) x 25^(2/3) ÷ 2^(5/3) = 5/4 (=1.25)

Answer 3

To solve this problem, use rules for exponents such as shown below:

a^-n=1/a^n=1^n/a^n=(1/a)^n (a≠0), a^mn=(a^m)^n, and a^m/b^m=(a/b)^m (b≠0), where a,b,m,n are any real numbers with the limitations listed.   Each term of the given equations can be written as follows:

10 to the negative one-third: 10^(-1/3)=1/10^(1/3)=(1/10)^(1/3), 25 to the two-thirds: 25^(2/3)=(25^2)^(1/3)=625^(1/3), and 2 to the five-thirds: 2^(5/3)=(2^5)^(1/3)=32^(1/3)   

Thus, this problem can be solved as follows:

10^(-1/3) x 25^(2/3) ÷ 2^(5/3) = (1/10)^(1/3) x 625^(1/3) ÷ 32^(1/3) = (1/10 x 625 ÷ 32)^(1/3)

= (625/(10x32))^(1/3) = (125/64)^(1/3) = (5^3/4^3)^(1/3) = ((5/4)^3)^(1/3) = (5/4)^(3x1/3) = (5/4)

Therefore, the answer is: 10^(1/3) x 25^(2/3) ÷ 2^(5/3) = 5/4 (=1.25)