which expression is equivalent to $64y^{18}-1000z^{6}$?\n$(4y^{6})^{3}-(10z^{2})^{3}$\n$(16y^{6})^{3}-(10z^{2…

which expression is equivalent to $64y^{18}-1000z^{6}$?\n$(4y^{6})^{3}-(10z^{2})^{3}$\n$(16y^{6})^{3}-(10z^{2})^{3}$\n$(16y^{6})^{3}-(100z^{2})^{3}$\n$(4y^{6})^{3}-(100z^{2})^{3}$

which expression is equivalent to $64y^{18}-1000z^{6}$?\n$(4y^{6})^{3}-(10z^{2})^{3}$\n$(16y^{6})^{3}-(10z^{2})^{3}$\n$(16y^{6})^{3}-(100z^{2})^{3}$\n$(4y^{6})^{3}-(100z^{2})^{3}$

Answer

Explanation:

Step1: Rewrite 64 and 1000 as perfect - cubes

We know that $64 = 4^3$ and $1000=10^3$. Also, using the power - of - a - power rule $(a^m)^n=a^{mn}$, for $y^{18}=(y^6)^3$ and $z^6=(z^2)^3$. So, $64y^{18}=(4y^6)^3$ and $1000z^6=(10z^2)^3$.

Step2: Rewrite the given expression

The expression $64y^{18}-1000z^6$ can be rewritten as $(4y^6)^3-(10z^2)^3$.

Answer:

$(4y^6)^3-(10z^2)^3$ (the first option)