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Use the properties of exponents to simplify the expression. (Shown in image)

Use The Properties Of Exponents To Simplify The Expression Shown In Image class=

Sagot :

Answer:[tex]\frac{y^{6}}{x^{2}}[/tex]Explanation:

The given expression is:

[tex](y^{\frac{3}{2}}x^{-\frac{1}{2}})^4[/tex]

Note from the rule of indices that:

[tex](ab)^c=a^cb^c[/tex]

Applying this rule to the given expression, we have:

[tex]\begin{gathered} y^{4(\frac{3}{2})}\times x^{-\frac{1}{2}(4)} \\ \end{gathered}[/tex]

This can be further simplified as:

[tex]\begin{gathered} y^{2(3)}\times x^{-2} \\ y^6x^{-2} \end{gathered}[/tex]

Therefore, the simplified expression is:

[tex]\frac{y^{6}}{x^{2}}[/tex]