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How do you evaluate the expression #(1/5)^-4/((1/5)^-2(1/5)^-5)# using the properties?

Answer 1

Genesis Allen

#1/125#

Set #x=1/5# to make things clearer

#x^(-4)/(x^(-2)x^(-5))#

#=x^(-4)/x^(-7)#

Note that #1/x^(-7)# is the same as #x^7#

Note that #x^(-4)# is the same as #1/x^4#

Putting it all together we have:

#x^7/x^4# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Method 1: #->x^(7-4)=x^3#

Method 2: #->1/(cancel(x^4))xx cancel(x^4)xxx^3" "=" "x^3#

Finally, replace #x# with #1/5# and simplify.

#x^3 = (1/5)^3 = 1^3/5^3 = 1/125#

Final Answer

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Answer 2

Eli Assouline

To evaluate the expression ((1/5)^{-4}/((1/5)^{-2}(1/5)^{-5})), you can use the properties of exponents.

Step 1: Simplify the exponents inside the parentheses separately. ((1/5)^{-2} = (5/1)^{2} = 25) ((1/5)^{-5} = (5/1)^{5} = 3125)

Step 2: Substitute the simplified values into the expression. ((1/5)^{-4}/((1/5)^{-2}(1/5)^{-5}) = (1/5)^{-4}/(25 * 3125))

Step 3: Simplify further. ((1/5)^{-4}/(25 * 3125) = (5/1)^{4}/(25 * 3125) = 625/78125)

Step 4: Evaluate the division. (625/78125 = 1/125)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.