What is #45^{-\frac{3}{2}}\times 45^{2}#?

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Answer 1 · 2016-10-02T02:24:54

#3sqrt5 ~= 6.7082#

Remember a law of indicies:

#a^mxxa^n = a^(m+n)#

In this example: #a=45, m=-3/2, n=2#

Hence #45^(-3/2)xx45^2 = 45^(-3/2+2)#

#=45^(1/2) = sqrt45#

# = sqrt(3xx3xx5) = 3sqrt5#

#~= 6.7082#