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Choose the expression that is equivalent to a fraction with seven raised to the negative third power in the numerator and the quantity three raised to the negative second power times seven squared end quantity in the denominator and the entire fraction is cubed.

need answer ASAP pls answer quick

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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