Help me with this one please. 11) Simplify the given expression using only positive exponents Show your work
7x^-4w^-7(-4x^3w^0)

Simplify:

1.  

4

−

2

2.  

10

−

3

Solution

1.  

4

−

2

Use the definition of a negative exponent,  

a

−

n

=

1

a

n

.  

1

4

2

Simplify.  

1

16

2.  

10

−

3

Use the definition of a negative exponent,  

a

−

n

=

1

a

n

.  

1

10

3

Simplify.  

1

1000

Step-by-step explanation: Simplify expressions with negative exponents

The Quotient Property of Exponents, introduced in Divide Monomials, had two forms depending on whether the exponent in the numerator or denominator was larger.

QUOTIENT PROPERTY OF EXPONENTS

If  

a

is a real number,  

a

≠

0

, and  

m

,

n

are whole numbers, then

a

m

a

n

=

a

m

−

n

,

m

>

n

and

a

m

a

n

=

1

a

n

−

m

,

n

>

m

What if we just subtract exponents, regardless of which is larger? Let’s consider  

x

2

x

5

.

We subtract the exponent in the denominator from the exponent in the numerator.

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent