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3 years ago

2. For a particular model of a car, a dealer offers 3 sizes of engines, 2 types of stereos, 18 body

Mathematics

1 answer:

Gnesinka [82]3 years ago

3 0

The given details follow the product rule. The different model of the car available are 756.

Given that:

$Engines = 3$

$Stereos = 2$

$Body=18$

$Color = 7$

The different possibility is calculated using the following product rule:

$Total =Engines \times Stereos \times Body \times Color$

So, we have:

$Total = 3\times 2\times 18 \times 7$

$Total = 756$

Hence, there are 756 different models available.

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Option B: $\sqrt[9]{xy^2}$

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Applying exponent rule, we get,

$x^{\frac{1}{9}} y^{\frac{2}{9}}$

Thus, the expression $\sqrt[9]{xy^2}$ is not equivalent to the expression $xy^{\frac{2}{9}}$

Hence, Option B is not the correct answer.

Option C: $x\sqrt{y^9}$

The expression can be written as $x(y^9)^{\frac{1}{2} }$

Applying exponent rule, we get,

$x y^{\frac{9}{2}}$

Thus, the expression $x\sqrt{y^9}$ is not equivalent to the expression $xy^{\frac{2}{9}}$

Hence, Option C is not the correct answer.

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The expression can be written as $x(y^2)^{\frac{1}{9} }$

Applying exponent rule, we get,

$xy^{\frac{2}{9}}$

Thus, the expression $xy^{\frac{2}{9}}$ is equivalent to the expression $xy^{\frac{2}{9}}$

Hence, Option D is the correct answer.

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