Question

Simplify 9³x9⁵=9[?]
Find the missing exponent​

Answer 1

`\huge\text{Hey there!}`

`\mathsf{9^3 * 9^5}\\\mathsf{= 9* 9 * 9\ \boxed{*}\ 9* 9* 9 * 9 * 9}\\\mathsf{= 81* 9\ \boxed{*}\ 81*81*9}\\\mathsf{= 729\ \boxed{*}\ 6,561* 9}\\\mathsf{= 729\ \boxed{*}\ 59,049}\\\mathsf{= 43,046,721}\\\mathsf{= 9^3 * 9^5 \rightarrow 9^(3 + 5)\rightarrow 9^8}`

`\huge\text{Therefore your answer should be:}`

`\huge\boxed{\mathsf{9^8}}\huge\checkmark`

~
`\frak{Amphitrite1040:)}`

Answer 2

`\large\boxed{\mathtt{9^(8)}}`

Explanation:

`\textsf{For this problem, we are asked to simplify the given expression.}`

`\textsf{Let's begin by understand an important rule for problems like these.}`

`\mathtt{9^(3) * 9^(5) = 9^(?)}`

`\large\underline{\textsf{We should remember that;}}`

`\textsf{When exponents multiply, they \underline{add}.}`

`\large\underline{\textsf{Why?}}`

`\textsf{If not, then the answer will be incorrect. Let's identify why in an example.}`

`\large\underline{\textsf{Bad Example:}}`

`\mathtt{2^(2) * 2^(5) = 2^(2 * 5 =10)}`

`\textsf{This means that;}`

`\mathtt{2 * 2 * 2 * 2 * 2 * 2 * 2 \\eq 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2.}`

`\large\underline{\textsf{Good Example:}}`

`\mathtt{2^(2) * 2^(5) = 2^(2+5=7)}`

`\textsf{This means that;}`

`\mathtt{2 * 2 * 2 * 2 * 2 * 2 * 2 = 2 * 2 * 2 * 2 * 2 * 2 * 2.}`

`\textsf{Let's follow the good example!}`

`{\mathtt{9^(3) * 9^(5) = 9^(3 + 5=8)}`

`\textsf{This means that;}`

`\mathtt{9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 = 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9.}`

`\large\boxed{\mathtt{9^(8)}}`