Question 151177
1. what is the product of (6x)squared and (2x) to the negative fourth power?
2. the base of a triangle is 5xy to the third and the height is 3x squared y, what is the area of a triangle?
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#1:
{{{ (6x)^2 * (2x)^(-4) }}}
"Power rules" says that when you have a negative power, you could move it to the denominator to make it a positive power.  Thus:
{{{ (6x)^2 /(2x)^4 }}}
Now, you can start reducing:
{{{ (36x^2) /(16x^4) }}}
{{{ (9x^2) /(4x^4) }}}
{{{ (9) /(4x^2) }}}
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#2:
I believe you are saying:
base is 5xy^3
height is 3x^2y
.
Area for any triangle is (1/2)bh
where
b is base
h is height
.
So, now we have:
{{{ (1/2)bh }}}
{{{ (1/2)(5xy^3)(3x^2y) }}}
{{{ (1/2)(5xy^4)(3x^2) }}}
{{{ (1/2)(5x^3y^4)(3) }}}
{{{ (15x^3y^4)/2 }}}

Please write back if my assumptions were incorrect.