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Working with Negative Exponents

[tex]\[ x^{-n}=\frac{1}{x^n} \quad \text{and} \quad \frac{1}{x^{-n}}=x^n \][/tex]

You can eliminate negative exponents by rewriting the expression as 1 divided by the variable or number raised to the related positive exponent.

Complete this expression:
[tex]\[ y^{-P} = \][/tex]
[tex]\[ \boxed{\phantom{placeholder}} \][/tex]

Simplify the following expression completely:
[tex]\[ 13v^{-7} = \][/tex]
[tex]\[ \boxed{\phantom{placeholder}} \][/tex]



Answer :

GinnyAnswer
Sure, let's go through the process of eliminating the negative exponents step-by-step.

### Step-by-Step Solution:

#### 1. Rewriting [tex]\( y^{-P} \)[/tex]:

A negative exponent indicates that the base is on the denominator. Specifically, for any variable [tex]\( y \)[/tex] raised to a negative exponent [tex]\( -P \)[/tex], it can be rewritten as:
[tex]\[ y^{-P} = \frac{1}{y^{P}} \][/tex]

So,
[tex]\[ y^{-P} = \frac{1}{y^P} \][/tex]

#### 2. Simplifying [tex]\( 13 v^{-7} \)[/tex]:

Similarly, for the expression [tex]\( 13 v^{-7} \)[/tex], the term [tex]\( v^{-7} \)[/tex] can be rewritten as [tex]\( \frac{1}{v^{7}} \)[/tex]. Therefore, the expression becomes:
[tex]\[ 13 v^{-7} = 13 \cdot \frac{1}{v^7} = \frac{13}{v^7} \][/tex]

So,
[tex]\[ 13 v^{-7} = \frac{13}{v^7} \][/tex]

### Final Answers:

1. [tex]\( y^{-P} = \frac{1}{y^P} \)[/tex]
2. [tex]\( 13 v^{-7} = \frac{13}{v^7} \)[/tex]

These are the simplified forms of the given expressions with the negative exponents eliminated.

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