Answer:
D) [tex]8g^{6} h^{4} k^{12} -h^{25}k^{15}[/tex]
Step-by-step explanation:
You have to use the laws of exponents to solve this:
Power of a Power: [tex](a^{m} )^{n} = a^{mn}[/tex]. In this case, [tex](4g^{3} h^{2} k^{4} )^{3}[/tex], all of the numbers in the parenthesis need to be multiplied to the power of 3: [tex]4^{3} g^{9} h^{6} k^{12}[/tex].
Quotient of Powers: [tex]\frac{a^{m} }{a^{n} } = a^{m-n}[/tex]. In this case, [tex]\frac{4^{3} g^{9} h^{6} k^{12}}{8g^{3} h^{2} }[/tex], all of the exponents need to be subtracted (but the 4³ (64) and 8 need to be divided): [tex]8g^{6} h^{4} k^{12}[/tex].
Use the Power of a Power again for the expression at the right: [tex](h^{5} k^{3} )^{5}[/tex]. You get: [tex]h^{25} k^{15}[/tex]. Keep the subtraction/negative sign where it is.
Together, you get: [tex]8g^{6} h^{4} k^{12} -h^{25}k^{15}[/tex].
Hope it helps!
