How do you simplify the expression #(1/32)^(-2/5)#?

Question

Eli Assouline · Accepted Answer

#(1/32)^(-2/5)=4#

To make this easier to solve, there's a rule that helps: #a^(mn)=(a^m)^n#, and what it basically says is that you can split up to the index/exponent (the small raised number) into smaller numbers which multiply to it, e.g. #2^6=2^(2*3)=(2^2)^3# or #2^27=2^(3*3*3)=((2^3)^3)^3#

Ok let's make that number less scary by spreading it out: #(1/32)^(-2/5)=(((1/32)^-1)^(1/5))^2# Now lets solve from the inside out. #=((32)^(1/5))^2# We can say this because: #(1/32)^-1=32/1=32#, and then we replace it within the equation. *Note: a '-1' exponent means to just flip the fraction or number*

#=(2)^2#

We can say this because #32^(1/5)=2# *Note: Unless you know logarithms, there's no way to know this other than using your calculator. Also, if the exponent is a fraction, it means to 'root' it e.g. #8^(1/3)=root3(2)#*

#=4#

The final and simple step

Savannah Anderson · Answer

undefined To simplify the expression (1/32)^(-2/5), you can first invert the fraction to make the exponent positive: 32^(2/5). Then, calculate the fifth root of 32, which is 2, and raise the result to the power of 2: 2^2 = 4. So, (1/32)^(-2/5) simplifies to 4.