Question

Simplify the expression. Write your answer using only positive exponents. Evaluate any numerical powers.

3^4⋅x⋅(3/x^2)^−2

show your work

Answer 1

`\\ \rm\Rrightarrow 3^4x\left((3)/(x^2)\right)^(-2)`

`\\ \rm\Rrightarrow 3^4x* \left(dfrac{x^2}{3}\right)^2`

`\\ \rm\Rrightarrow 3^4x*(x^4)/(3^2)`

• a^m×a^n=a^m+n
• a^m/a^n=a^m-n

`\\ \rm\Rrightarrow 3^2x^5`

`\\ \rm\Rrightarrow 9x^5`

Answer 2

• 9x⁵

Explanation:

Use properties of exponents:

• 
  `a^(b) a^(c) = a^(b+c)`,
  `(a^(b) ^)^(c) = a^(bc)`,
  `1/a^(-b) = a^(b)`

Simplify the given expression:

• 3⁴⋅x⋅(3/x²)⁻² =
• 3⁴·x·(3x⁻²)⁻² =
• 3⁴·x·(3⁻²)(x⁻²ˣ⁻²) =
• 3⁴⁻²·x¹⁺4 =
• 3²·x⁵ =
• 9x⁵