Exponent Laws Related Homework Question

In summary, the conversation discusses solving an equation and determining the non-zero value of x for which the equation is true. The use of the guess and check method is mentioned, but the person is looking for a faster method. It is concluded that there is no value for which the equation is true and negative values such as -1 do not work. The person is advised to simplify the equation, which leads to the conclusion that the equation is not true for any value of x. The person then thanks the other party for their help but then asks if negative values could work, despite already understanding that no value works.
  • #1
pandamonium786
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Homework Statement


For which non-zero value of x is the equation -x^ -4 = (-x)^ -4 true? Explain.

Homework Equations


None. Other than applicable exponent laws.

The Attempt at a Solution


I know how to use the guess and check method. But I was wondering how to reach the answer faster and how to solve this problem.
 
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  • #2
There is no value for which it is true.Try and prove it.
 
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  • #3
LittleMrsMonkey said:
There is no value for which it is true.Try and prove it.

i understand that but could negative numbers like -1 work?
 
  • #4
If you raise any negative to an even power(like -4) it gives something positive.
 
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  • #5
Try to simplify the equation,you will get to -1=1,which of course isn't true.So the equation isn't true for any x.
 
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  • #6
LittleMrsMonkey said:
Try to simplify the equation,you will get to -1=1,which of course isn't true.So the equation isn't true for any x.

Thanks again :D
 
  • #7
pandamonium786 said:
i understand that but could negative numbers like -1 work?
How can you possibly say "I understand" that no value works and then ask if a negative value works?
 

Related to Exponent Laws Related Homework Question

1. What are the basic exponent laws?

The basic exponent laws include the product law, quotient law, power law, zero exponent law, and negative exponent law. The product law states that when multiplying two powers with the same base, you add the exponents. The quotient law states that when dividing two powers with the same base, you subtract the exponents. The power law states that when raising a power to another power, you multiply the exponents. The zero exponent law states that any number (except 0) raised to the 0 power is equal to 1. The negative exponent law states that any number raised to a negative exponent can be rewritten as the reciprocal of the number raised to the positive exponent.

2. How do I simplify expressions with exponents?

To simplify expressions with exponents, you can use the exponent laws mentioned above. Start by applying the product or quotient law, if applicable. Then, simplify any exponents using the power law, zero exponent law, or negative exponent law. Keep applying these laws until the expression is in its simplest form.

3. What is the difference between a power and an exponent?

A power is an expression that represents repeated multiplication, while an exponent is the number that indicates how many times the base is multiplied by itself in a power. For example, in the expression 23, 2 is the base and 3 is the exponent.

4. How do I solve equations with exponents?

To solve equations with exponents, you can use the exponent laws and algebraic properties of equality. Start by simplifying each side of the equation using the exponent laws. Then, isolate the variable by using inverse operations, such as dividing or multiplying, to get the variable alone on one side of the equation.

5. Can I apply exponent laws to any type of number?

Yes, you can apply exponent laws to any type of number, including whole numbers, fractions, decimals, and negative numbers. The laws work the same way regardless of the type of number being used.

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