The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.
The given expression is [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex].
We need to find the equivalent expression for the given expression.
What is an equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Now, [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex] using [tex]a^{m} \times a^{n}=a^{m+n}[/tex].
We get, [tex]((\frac{2}{3} )^{4+3})^{2}=((\frac{2}{3} )^{7})^{2}[/tex]
Using the exponents rule [tex](a^{m} )^{n}=a^{m\times n}[/tex]
=[tex]=(\frac{2}{3} )^{7\times 2}=(\frac{2}{3} )^{14}[/tex]
The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.
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