[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\large\textbf{Which expression is equivalent to }\rm{\bf 5^{10} \times 5^5}\large\textbf{ ?}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{5^{10}\times5^5}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathbf{5^{10}\times5^5}[/tex]
[tex]\huge\textbf{Simplifying the exponents:}[/tex]
[tex]\mathbf{5^{10}}\\\\\mathbf{= 5\times5\times5\times5\times5\times5\times5\times5\times5\times5}\\\\\mathbf{= 25\times25\times25\times25\times25}\\\\\mathbf{= 625 \times 625 \times 25}\\\\\mathbf{= 390,625 \times 25}\\\\\mathbf{= 9,765,625}[/tex]
[tex]\mathbf{5^5}\\\\\mathbf{= 5\times5\times5\times5\times5}\\\\\mathbf{= 25\times25\times5}\\\\\mathbf{= 625\times5}\\\\\mathbf{= 3,125}[/tex]
[tex]\huge\textbf{Temporary equation: }[/tex]
[tex]\mathbf{9,765,625 \times 3,125}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{= 30,517,578,125}[/tex]
[tex]\huge\textbf{Now, let's do process of elimination}\\\\\huge\textbf{to see which one answers the overall}\\\\\huge\textbf{question:}[/tex]
[tex]\huge\text{Option A.}\\\\\\\mathsf{5^2}\\\\\mathsf{= 5\times 5}\\\\\mathsf{= 25}\\\\\huge\textsf{Option A. is incorrect because it isn't}\\\huge\textsf{equivalent to your given equation.}[/tex]
[tex]\huge\text{Option B.}\\\\\\\mathsf{5^5}\\\\\mathsf{= 5\times 5\times5 \times5\times5}\\\\\mathsf{= 25\times25\times5}\\\\\mathsf{= 625\times5}\\\\\mathsf{= 3,125}\\\\\huge\textsf{Option B. is incorrect because it isn't}\\\huge\textsf{equivalent to your given equation.}[/tex]
[tex]\huge\text{Option C.}\\\\\mathsf{5^{15}}\\\\\mathsf{= 30,517,578,125}\\\\\huge\textsf{Option C. could possibly be your answer.}[/tex]
[tex]\huge\text{Option D.}\\\\\mathbf{5^{50}}\\\\\large\textsf{Since, }\mathsf{5^{50}}\large\textsf{ is too big to count we will say the approximation is:}\\\large\textsf{8.8817841970013e + 34 (We couldn't put the exact number because}\\\large\textsf{it is too big so we had to label it as that estimation)}\\\\\\\huge\textsf{Anyway, Option D. is not your answer.}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{5^{15}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
