SOLUTION: Simplifying rational exponents; negative exponents and fractional bases. I don't understand these problems and need step by step instruction to complete remaining homework. Need

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Question 948626: Simplifying rational exponents; negative exponents and fractional bases. I don't understand these problems and need step by step instruction to complete remaining homework. Need to simplify and write without exponents. Please and thank you.
(1/25)^3/2=?
64^-2/3
I appreciate your assistance with the step by step instruction. :)
Found 3 solutions by Fombitz, MathLover1, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1.
%281%2F25%29%5E%283%2F2%29-> exponent 3%2F2 means square root of a number to the power of 3
so, you have
%281%2F25%29%5E%283%2F2%29
=sqrt%28%281%2F25%29%5E3%29%29
=sqrt%281%5E3%29%2Fsqrt%2825%5E3%29
=1%2Fsqrt%28%285%5E2%29%5E3%29
=1%2Fsqrt%285%5E2%2A5%5E2%2A5%5E2%29
=1%2F%285%2A5%2A5%29
=1%2F125
in decimal form: 0.008

2.
64%5E-2%2F3 here you have negative exponent-%282%2F3%29 and to get positive exponent write inverse: -%282%2F3%29=1%2F%282%2F3%29
so, you have
64%5E-2%2F3
=1%2F%2864%5E%282%2F3%29%29
=1%2F%28root%283%2C64%5E2%29%29...you can write 64%5E2 as 8%5E2%2A8%5E2,then
=1%2F%28root%283%2C%284%5E3%2A4%5E3%29%29%29
=1%2F%284%2A4%29
=1%2F16
or as decimal 0.0625


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Simplifying rational exponents; negative exponents and fractional bases. I don't understand these problems and need step by step instruction to complete remaining homework. Need to simplify and write without exponents. Please and thank you.
(1/25)^3/2=?
64^-2/3
I appreciate your assistance with the step by step instruction. :)


I.

%281%2F25%29%5E%283%2F2%29

%285%5E%28-+2%29%29%5E%283%2F2%29 ------- 1%2F25 is the same as 5%5E-2

highlight%28highlight%285%5E%28-+2%283%2F2%29%29%29%29 ------ Exponents are multiplied when raising an expression with the same base

                    to another power (- 2 being raised to the 3%2F2)

highlight%28highlight%285%5E%28%28-+cross%282%29%29%283%2Fcross%282%29%29%29%29%29_____5%5E-+3________highlight_green%28highlight_green%281%2F125%29%29%29





II.

64%5E%28-+2%2F3%29________%28root%283%2C+64%29%29%5E%28-+2%29_______4%5E-+2________1%2F4%5E2_______highlight_green%281%2F16%29