Question

Which expression is equivalent to quantity y raised to the negative second power times z raised to the seventh power end quantity over quantity z raised to the negative third power times y raised to the eighth power end quantity all raised to the negative second power?

Answer 1

The expression that is equivalent to the given expression is y²⁰z⁻²⁰

Evaluating an expression

From the question, we are to find the expression that is equivalent to the given expression

The given expression is

$(\frac{y^{-2}z^{7} }{z^{-3} y^{8} }) ^{-2}$

Simplifying

$(\frac{y^{-2}z^{7} }{z^{-3} y^{8} }) ^{-2}$

From one of the laws of indices, we have that

$(\frac{x}{y} )^{-z} = (\frac{y}{x} )^{z}$

Thus,

$(\frac{y^{-2}z^{7} }{z^{-3} y^{8} }) ^{-2}$  becomes

$(\frac{z^{-3} y^{8} }{y^{-2}z^{7} }) ^{2}$

Then,

$(\frac{z^{-3} }{z^{7} } \times \frac{y^{8}}{y^{-2}} ) ^{2}$

$(z^{-3-7}} \times y^{8--2}} ) ^{2}$

$(z^{-10}} \times y^{8+2}} ) ^{2}$

$(z^{-10}} \times y^{10}} ) ^{2}$

$(z^{-10 \times 2}} \times y^{10 \times 2}} )$

$(z^{-20}} \times y^{20}} )$

$z^{-20}} y^{20}}$

= $y^{20}} z^{-20}}$

OR

= $\frac{y^{20} }{z^{-20}}$

Hence, the expression that is equivalent to the given expression is y²⁰z⁻²⁰

Learn more on Evaluating an expression here: https://brainly.com/question/28058543

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