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


3^4⋅x⋅(3/x^2)^−2

show your work

Sagot :

mhanifa

Answer:

  • 9x⁵

Step-by-step explanation:

Use properties of exponents:

  • [tex]a^{b} a^{c} = a^{b+c}[/tex], [tex](a^{b} ^)^{c} = a^{bc}[/tex], [tex]1/a^{-b} = a^{b}[/tex]

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

MisterBrainly

[tex]\\ \rm\Rrightarrow 3^4x\left(\dfrac{3}{x^2}\right)^{-2}[/tex]

[tex]\\ \rm\Rrightarrow 3^4x\times \left(dfrac{x^2}{3}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow 3^4x\times\dfrac{x^4}{3^2}[/tex]

  • a^m×a^n=a^m+n
  • a^m/a^n=a^m-n

[tex]\\ \rm\Rrightarrow 3^2x^5[/tex]

[tex]\\ \rm\Rrightarrow 9x^5[/tex]

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