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Sagot :
The expression that is equivalent to the given expression is 3⁶/7¹⁵
Simplifying an expression
From the question, we are to determine the expression that is equivalent to the given expression
The given expression is
[tex]\left(\frac{7^{-3} }{3^{-2} \times 7^{2}} \right)^{3}[/tex]
Simplifying
[tex]\left(\frac{7^{-3} }{3^{-2} \times 7^{2}} \right)^{3}[/tex]
[tex]\left(\frac{7^{-3 \times 3} }{3^{-2 \times 3} \times 7^{2 \times 3}} \right)[/tex]
[tex]\left(\frac{7^{-9} }{3^{-6} \times 7^{6}} \right)[/tex]
= [tex]\left( 7^{-9} \times \frac{1}{3^{-6}} \times \frac{1 }{7^{6}} \right)[/tex]
= [tex]\left( \frac{1}{7^{9} } \times 3^{6} \times \frac{1 }{7^{6}} \right)[/tex]
= [tex]\left(\frac{3^{6} }{7^{9} \times 7^{6}} \right)[/tex]
= [tex]\frac{3^{6} }{7^{9+6}}[/tex]
= [tex]\frac{3^{6} }{7^{15}}[/tex]
Hence, the expression that is equivalent to the given expression is 3⁶/7¹⁵
Learn more on Simplifying an expression here: https://brainly.com/question/15361818
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