Question

I need help take your time not in that big of a rush

Answer 1

Given Equation:-

$\boxed{ \sf \frac{ \sf 15 {x}^{ - 3} {y}^{2} {z}^{ - 6} }{6 {x}^{5} {y}^{ - 2} {z}^{ - 4} } }$

Step by step expansion:-

$\dashrightarrow\sf \dfrac{ \sf 15 {x}^{ - 3} {y}^{2} {z}^{ - 6} }{6 {x}^{5} {y}^{ - 2} {z}^{ - 4} }$

First of all write the equation which is given in question. like this you won't do any minor mistakes of writing wrong digits while calculating.

$\dashrightarrow\sf \dfrac{ \sf3 \times 5 {x}^{ - 3} {y}^{2} {z}^{ - 6} }{3 \times 2 {x}^{5} {y}^{ - 2} {z}^{ - 4} }$

Simply 15 and 6 . where 15 is in numerator and 6 is in denominator.

$\dashrightarrow\sf \dfrac{ \sf\cancel3 \times 5 {x}^{ - 3} {y}^{2} {z}^{ - 6} }{\cancel3 \times 2 {x}^{5} {y}^{ - 2} {z}^{ - 4} }$

So after simplifying we get to know digit 3 is present both in numerator and denominator, that's why we have canceled it.

$\dashrightarrow\sf \dfrac{ \sf 5 {x}^{ - 3} {y}^{2} {z}^{ - 6} }{2 {x}^{5} {y}^{ - 2} {z}^{ - 4} }$

Write the equation after canceling 3 which was present both in numerator and denominator.

$\dashrightarrow\sf \dfrac{ \sf 5 {x}^{0} {y}^{2} {z}^{ - 6} }{2 {x}^{5 + 3} {y}^{ - 2} {z}^{ - 4} }$

transfer power of x which is -3 in numerator and add with the x with power 5 in denominator.

$\dashrightarrow\sf \dfrac{ \sf 5 {y}^{2} {z}^{ - 6} }{2 {x}^{8} {y}^{ - 2} {z}^{ - 4} }$

After adding power of x we get x⁸ as product.

$\dashrightarrow\sf \dfrac{ \sf 5 {y}^{2} {z}^{0} }{2 {x}^{8} {y}^{ - 2} {z}^{ - 4 + 6} }$

Now transfer power of z which is numerator as 6 .

$\dashrightarrow\sf \dfrac{ \sf 5 {y}^{2}}{2 {x}^{8} {y}^{ - 2} {z}^{2} }$

after adding power we got z² as productive.

$\dashrightarrow\sf \dfrac{ \sf 5 {y}^{2 + 2}}{2 {x}^{8} {y}^{0} {z}^{2} }$

Now transfer value of y I.e - 2 in denominator to numerator with power 2. Now u probably thinking why with x and z we have transfered power from numerator to denominator while in y denominator to numerator. that's because we always want power in positive.

$\dashrightarrow\bf \dfrac{ 5 {y}^{4}}{2 {x}^{8} {z}^{2} }$

Finally we got our result .

Option A is correct!

Answer 2

Applying division of terms with the same base and different exponents, it is found that the simplified expression is given by:

$\frac{5y^4}{2x^8z^2}$

What is the property of the division of terms with the same base and different exponents?

We keep the base and subtracted the exponents, that is:

$\frac{x^a}{x^b} = x^{a - b}$

In this problem, we simplify the coefficients and each letter separately, hence:

$\frac{15}{6} = \frac{5}{2}$

$\frac{x^{-3}}{x^5} = x^{-3 - 5} = x^{-8} = \frac{1}{x^8}$

$\frac{y^2}{y^{-2}} = y^{2 - (-2)} = y^4$

$\frac{z^{-6}}{z^{-4}} = z^{-6 - (-4)} = z^{-2} = \frac{1}{z^2}$

Then, multiplying the results of these expressions, the simplified expression is given by:

$\frac{5y^4}{2x^8z^2}$

More can be learned about the division of terms with the same base and different exponents at https://brainly.com/question/14300274