Negative Exponents: Solve the Problem and Figure it Out

In summary, the conversation is about understanding negative exponents and solving a specific problem using substitution. The solution is obtained by multiplying the expression by a certain factor.
  • #1
Circe
1
0
I hope I'm doing this correctly!

I'm having problems understanding negative exponents and how they work...

I have this problem, (x^-2)/(x^-2 + y^-2)

I don't understand how the answer could be, (y^2)/(x^2 + y^2)..

Maybe I'm doing something incorrectly? :/
 
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  • #2
Circe said:
I hope I'm doing this correctly!

I'm having problems understanding negative exponents and how they work...

I have this problem, (x^-2)/(x^-2 + y^-2)

I don't understand how the answer could be, (y^2)/(x^2 + y^2)..

Maybe I'm doing something incorrectly? :/

welcome on MHB Circe!...

For the solution is sufficient the substitution $\displaystyle x^{- 2} = \frac{1}{x^{2}}$ and $\displaystyle y^{- 2} = \frac{1}{y^{2}}$ ...

Kind regards

$\chi$ $\sigma$
 
  • #3
Try multiplying the expression by:

\(\displaystyle \frac{x^2y^2}{x^2y^2}\)

And see what you get...:D
 

FAQ: Negative Exponents: Solve the Problem and Figure it Out

What are negative exponents and how do they work?

Negative exponents are a mathematical concept that represents the reciprocal of a number raised to a positive exponent. For example, 2-3 is the same as 1/23. Negative exponents follow the rule that x-n = 1/xn. This means that the base number is moved to the opposite side of the fraction and the exponent becomes positive.

How do I solve a problem with negative exponents?

Solving a problem with negative exponents involves applying the rule that x-n = 1/xn. This means that you can move the base number to the opposite side of the fraction and change the sign of the exponent to make it positive. Once you have done this, you can simplify the expression by evaluating the power. For example, 2-3 can be rewritten as 1/23 which evaluates to 1/8.

What happens when there are negative exponents in both the numerator and denominator?

When there are negative exponents in both the numerator and denominator, you can simplify the expression by moving the base numbers to the opposite side of the fraction and changing the signs of the exponents to make them positive. Then, you can simplify the expression by evaluating the powers. If the resulting fraction has a negative exponent in the denominator, you can move the base number to the numerator and change the sign of the exponent to make it positive.

Can negative exponents be used with any number?

Yes, negative exponents can be used with any number, including whole numbers, fractions, decimals, and even negative numbers. As long as the base number is not equal to zero, negative exponents can be applied according to the rule x-n = 1/xn.

Why are negative exponents important in scientific calculations?

Negative exponents are important in scientific calculations because they allow us to represent very small numbers in a more convenient way. For example, instead of writing 0.000001, we can write 10-6 which is much easier to work with. Negative exponents also come up in many scientific equations and formulas, so understanding how to use them is essential for accurate calculations.

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