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Which is an equivalent expression for five sevenths squared times one third raised to the power of negative three all raised to the power of negative one?

five sevenths squared times one third raised to the power of negative three
five sevenths times one third raised to the power of negative four
seven fifths to the power of negative two times one third to the power of negative three
seven fifths squared times one third cubed

Respuesta :

Medunno13

[tex]\left(\left(\frac{5}{7} \right)^2 \left(\frac{1}{3} \right)^{-3} \right)^{-1} \\ \\ =\left(\frac{5}{7} \right)^{-2} \left(\frac{1}{3} \right)^{3} \\ \\ =\boxed{\left(\frac{7}{5} \right)^2 \left(\frac{1}{3} \right)^3}[/tex]

The equivalent expressions are (5/7)⁻² (1/3)³ = (7/5)²  (1/3)³ .

What are equivalent expressions?

Equivalent expressions are expressions that work the same even though they look different. If the two algebraic expressions are equivalent, then the two expressions have the same value when we put in the same values for the variables.

Now the given expression is,

{(5/7)² (1/3)⁻³}⁻¹

using the property

(aⁿ)ˣ = aⁿˣ

This can be written as,

(5/7)⁻² (1/3)³

or,(5/7)⁻² (1/3)³ = (7/5)²  (1/3)³

which is seven fifths squared times one third cubed.

Hence,the equivalent expressions are (5/7)⁻² (1/3)³ = (7/5)²  (1/3)³ .

To learn more about equivalent expressions :

https://brainly.com/question/20055044

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