Question

I need help simplifying #6

Answer 1

Answer:

The simplified expression is $\frac{12x^8y^5}{5z^4}$

Therefore $\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}$

Step-by-step explanation:

Given expression is $\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}$

To simplify the given expression as below :

$\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}$

$=\frac{12x^5y^9z^{-8}}{5x^{-3}y^4z^{-4}}$

$=\frac{12x^5y^9z^{-8}x^3y^{-4}z^4}{5}$  ( by using the property $a^{m}=\frac{1}{a^{-m}}$ )

$=\frac{12x^5.x^3.y^9.y^{-4}z^{-8}z^4}{5}$

$=\frac{12}{5}x^{5+3}.y^{9-4}.z^{-8+4}$ ( by using the property $a^m.a^n=a^{m+n}$ )

$=\frac{12}{5}x^8y^5z^{-4}$

$=\frac{12x^8y^5}{5z^4}$  ( by using the property $a^{-m}=\frac{1}{a^m}$ )

$\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}$

The simplified expression is $\frac{12x^8y^5}{5z^4}$

Therefore $\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}$

Answer 2

Answer:

Therefore,

$\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}$

Step-by-step explanation:

Simplify

$\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}$

Solution:

Using the Identities

$1.\ x^{-a}=\dfrac{1}{x^{a}}$

$2.\ \dfrac{1}{x^{-a}}=x^{a}$

$3.\ \dfrac{x^{a}}{x^{b}}=x^{(a-b)}$

Therefore,

$\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{24x^{(5+3)}y^{(9-4)}z^{(-8+4)}}{10}$

$\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{2\times 12x^{8}y^{5}z^{-4}}{2\times 5}$

$\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}$

Therefore,

$\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}$