3 years ago

Activity 1 What is the value of the 3 in each of these numbers?

Mathematics

1 answer:

dusya [7]3 years ago

4 0

Answer: A OR E

Step-by-step explanation:

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Step-by-step explanation:

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Which expression is equivalent to \frac{10q^5w^7}{2w^3}.\ \frac{4\left(q6\right)^2}{w^{-5}} for all values of q and w where the

mestny [16]

Answer:

$\frac{10q^5w^7}{2w^3}.\ \frac{4\left(q^6\right)^2}{w^{-5}} =20q^{17}w^9$

Step-by-step explanation:

Given

$\frac{10q^5w^7}{2w^3}.\ \frac{4\left(q^6\right)^2}{w^{-5}}$

Required

Determine the equivalent expression

$\frac{10q^5w^7}{2w^3}.\ \frac{4\left(q^6\right)^2}{w^{-5}}$

Simplify the first fraction

$\frac{5q^5w^7}{w^3}.\ \frac{4\left(q^6\right)^2}{w^{-5}}$

Apply law of indices on the first fraction;

$5q^5w^{7-3}.\ \frac{4\left(q^6\right)^2}{w^{-5}}$

$5q^5w^4.\ \frac{4\left(q^6\right)^2}{w^{-5}}$

$\ \frac{5q^5w^4*4\left(q^6\right)^2}{w^{-5}}$

Apply law of indices:

$5q^5w^4*4\left(q^6\right)^2 * w^{5}$

Evaluate the bracket

$5q^5w^4*4 * q^{12} * w^{5}$

Collect Like Terms

$5*4q^5* q^{12}*w^4 * w^{5}$

$20q^5* q^{12}*w^4 * w^{5}$

$20q^{5+12}*w^{4+5}$

$20q^{17}w^9$

Hence:

$\frac{10q^5w^7}{2w^3}.\ \frac{4\left(q^6\right)^2}{w^{-5}} =20q^{17}w^9$

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