Question

Practice simplifying rational expressions with negative exponents.

Answer 1

Answer:

Part 1:- option first is correct

$-\frac{1}{2}ab^{12}$

Part 1:- option third is correct

$\frac{w^{10}}{3y^{4}}$

Step-by-step explanation:

Given:

The given ration expressions are.

1. $\frac{-2a^{2}b^{4}}{4ab^{-8}}$

2. $\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}$

We need to simplify the given expressions.

Solution:

Part 1:-

Given expression is

$=\frac{-2a^{2}b^{4}}{4ab^{-8}}$

Using law of exponents $\frac{x^{m} }{x^{n} } = x^{(m-n)}$

$=-\frac{a^{2-1}b^{4-(-8)}}{2}$

$=-\frac{a^{1}b^{4+8}}{2}$

$=-\frac{ab^{12}}{2}$

$=-\frac{1}{2}ab^{12}$

Therefore, option first $-\frac{1}{2}ab^{12}$ is correct.

Part 2:-

Given expression is.

$=\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}$

Using law of exponents $\frac{x^{m} }{x^{n} } = x^{(m-n)}$

$=\frac{w^{4-(-6)}y^{-2-2}}{3}$

$=\frac{w^{4+6}y^{-4}}{3}$

$=\frac{w^{10}y^{-4}}{3}$

$=\frac{w^{10}}{3y^{4}}$

Therefore, third option $\frac{w^{10}}{3y^{4}}$ is correct.