Question

Describe how you would simplify the given expression.

Answer 1

Answer:

Hence, the value of the simplified expression is:

$\dfrac{x^{-24}y^{15}}{64}$

Step-by-step explanation:

We  have to simplify $(\dfrac{20x^5y^2}{5x^{-3}y^7})^{-3}$

first we simplify the terms inside the bracket

20/5=4

As we know that:

$\dfrac{a^m}{a^n}=a^{m-n}$

$\dfrac{x^5}{x^{-3}}=x^8\\ \\\dfrac{y^2}{y^7}=y^{-5}$

$(4x^8y^{-5})^{-3}\\\\=\dfrac{x^{-24}y^{15}}{64}$

Hence, the expression that is obtained after simplification is:

$\dfrac{x^{-24}y^{15}}{64}$

Answer 2

Deal with the expression in the parentheses first.

20 / 5 = 4
x^5 / x^-3  = x^8
y^2/y^7 = y^-5  so we have

(4x^8 y^-5)^-3

= 1/64 * x^-24 y^15     which can be written as:_

    y^15
-----------
  64 x^24