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4 years ago

-1(75-y) as distributive property

1 answer:

4 0

Distributing -1 to (75 - y) just means taking each individual term within the parentheses (75 and -y respectively) and multiplying each by -1.

-1(75) = -75

-1(-y) = y

We're left with -75 + y

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ioda

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3 years ago

Read 2 more answers

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prohojiy [21]

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3 years ago

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Lesechka [4]

Option D:

$\frac{25 a^{9} b^{10} }{6 }$ is equivalent to the given expression.

Solution:

Given expression:

$$\frac{(5 a b)^{3}}{30 a^{-6} b^{-7}}$

To find which expression is equivalent to the given expression.

$$\frac{(5 a b)^{3}}{30 a^{-6} b^{-7}}$

Using exponent rule: $(ab)^m=a^mb^m$

$$=\frac{5^3 a^3 b^{3}}{30 a^{-6} b^{-7}}$

Using exponent rule: $\frac{1}{a^{m}}=a^{-m}, \quad \frac{1}{a^{-m}}=a^{m}$

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$$=\frac{125 a^3 a^{6} b^{3} b^{7}}{30 }$

Using exponent rule: $a^{m} \cdot a^{n}=a^{m+n}$

$$=\frac{125 a^{3+6} b^{3+7} }{30 }$

$$=\frac{125 a^{9} b^{10} }{30 }$

Divide both numerator and denominator by the common factor 5.

$$=\frac{25 a^{9} b^{10} }{6 }$

$$\frac{(5 a b)^{3}}{30 a^{-6} b^{-7}}=\frac{25 a^{9} b^{10} }{6 }$

Therefore, $\frac{25 a^{9} b^{10} }{6 }$ is equivalent to the given expression.

Hence Option D is the correct answer.

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barxatty [35]

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Lunna [17]

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3 years ago