Question

Maths question. Please explain how you got your answer.

Thank you :)

Answer 1

Answer:5/2=2.5

Explanation:

`√(27)=\sqrt{3^(3)}=3^(3)/(2)\\\\we \ can \ show \ \sqrt{3^(3)} \ as \ 3^(3)/(2)\\3^(1)*3{(3)/(2)}=3^{1+(3)/(2)}=3^{(5)/(2)}\\n=(5)/(2)`

Answer 2

`n=(5)/(2)`

Explanation:

Rewrite 27 as the product of prime numbers:

`\implies 27 = 3 \cdot 3 \cdot 3 = 3^3`

Therefore, replace 27 with 3³ in the given equation:

`\implies 3 * √(3^3)=3^n`

`\textsf{Apply the exponent rule:} \quad \sqrt[n]{a^m}=a^{(m)/(n)}`

`\implies 3 * 3^{(3)/(2)}=3^n`

`\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^(b+c)`

`\implies 3^1 * 3^{(3)/(2)}=3^n`

`\implies 3^{1 +(3)/(2)}=3^n`

`\implies 3^{(2)/(2) +(3)/(2)}=3^n`

`\implies 3^{(5)/(2)}=3^n`

`\textsf{Apply the exponent rule:} \quad a^(f(x))=a^(g(x)) \implies f(x)=g(x)`

`\implies (5)/(2)=n`

Therefore, the value of n is 5/2.