Question 1092943: Use the properties of exponents to simplify the expression.
(5^2)(5^-3) =
If would be great if you could please explain why the answer is 1/5.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 5^2 * 5^-3 = 5^2 / 5^3 = 5^(2-3) = 5^-1 = 1/5^1 = 1/5
this has to do with properties of exponents.
the rule is:
x^(-a) is equal to 1 / x^a
x^a is equal to 1 / x^(-a)
therefore:
5^2 * 5^(-3) is equal to 5^2 * 1 / 5^3 which is equal to 5^2 / 5^3.
another rule is:
x^a / x^b = x^(a-b)
therefore:
5^2 / 5^3 is equal to 5^(2-3) which is equal to 5^(-1) which is equal to 1/5.
here's some good references on exponent arithmetic.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut29_negexp.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut23_exppart1.htm
in fact, this website has many tutorials that are hugely helpful as tutorials and as references.
here's the main website.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm
on the questions of negative exponents, here's some more useful information.
if the negative exponents is in the numerator, then place it in the denominator and make the exponent positive.
if the negative expnent is in the denominator, then place it in the numerator and make the exponent positive.
example:
5^(-3) / 5^(-5) = 5^5 / 5^3 = 5^(5-3) = 25
this could also have been solved without doing that because:
5^(-3) / 5^(-5) = 5^(-3 - (-5)) = 5^(-3 + 5) = 5^2 = 25
note that numerator and denominator are always there but implied because:
any number by itself has a denominator of 1 and is also multiplied by 1.
therefore 5^(-3) = (1 * 5^(-3)) / 1.
place it in the denominator and make the exponent positive and you have 1 / (5^3 * 1) which simplifies to 1 / 5^3.
practice a few and you should have it in reasonably short period of time.
don't foget to study the references and to do the sample questions as well.
this allows you to solidify your learning.
here's 1 last example:
25x^-3 is equal to 25/x^3.
the 25 stays on top because it has a positive exponent which is 1, since any number raised to the power of 1 is that same number.
the x^-3 goes to the denominator and the exponent is made positive.
note that the rationale for moving it to the denominator is as follows:
25 * x^3 is equal to 25 * 1 / x^3 which is equal to (25 * 1) / x^3 which is equal to 25 / x^3
likewise x^-3 / y^-3 is equal to (1/x^3) / (1/y^3) which is equal to (1/x^3) * (y^3/1) which is equal to (1 * y^3) / (x^3 * 1) which is equal to y^3 / x^3.
send me an email if you have any further questions on this
|
|
|
