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A negative exponent becomes positive in the reciprocal.

So if you have a number a^x where x is negative, then,

a^x = 1/(a^-x) and, since x is negative, -x is positive.

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11y ago

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Simplify and write the answer in exponential notation using positive exponents 24 2 -2?

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A base raised to a negative power is equal to 1 divided by that base raised to a positive exponent. So 16 raised to (-3/2) is equal to 1/ (16 raised 3/2), or 1/64.


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First: You don't want any negative exponents. I'll give two examples- 5^-2 / 5^2. What you would do is switch the negative exponent to the other side, changing the negative exponent to a positive, and if there's nothing there, replace it with a one. So, now you have 1/ 5^2 * 5^2. Simplify 1/ 25 * 25 1/625. There's your answer. With variables: x^2 / y^-3. Switch the negative to a positive, placing it on the other side. Since the denominator becomes one and all you have are numerators, the denominator isn't needed (but you can still use it while learning the concept). x^2 * y^3. A fully simplified answer. I hope this helps!


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Related Questions

How do you simplify negative numbers with positive exponents?

If the exponent is an even number you can drop the negative, because is you were to multiply it out the negatives would cancel out.


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Combining laws of exponents refers to the rules that govern the manipulation of expressions involving powers. Key laws include the product of powers (adding exponents when multiplying like bases), the quotient of powers (subtracting exponents when dividing like bases), and the power of a power (multiplying exponents when raising a power to another power). These rules help simplify expressions and solve equations involving exponents efficiently. Understanding these laws is essential for working with algebraic expressions in mathematics.


How do you solve negative exponents equations with different bases?

To solve equations with negative exponents and different bases, first rewrite each term with a positive exponent by applying the rule (a^{-n} = \frac{1}{a^n}). This may involve moving terms across the equation. Once all terms have positive exponents, you can simplify or solve the equation by isolating the variable or using logarithms, if necessary. Finally, check for extraneous solutions, especially if you manipulated the equation significantly.


What is negative power?

Negative power refers to exponents that are less than zero, which represent the reciprocal of the base raised to the absolute value of the exponent. For example, ( a^{-n} ) equals ( \frac{1}{a^n} ) for any non-zero base ( a ) and positive integer ( n ). This concept is commonly used in mathematics and science, particularly in calculations involving fractions and inverse relationships. Negative powers help simplify expressions and solve equations effectively.


Can an exponent be a negative number?

Yes, an exponent can be a negative number. When a base is raised to a negative exponent, it is equivalent to taking the reciprocal of the base raised to the positive exponent. For example, ( a^{-n} = \frac{1}{a^n} ) where ( a ) is a non-zero number and ( n ) is a positive integer. This concept is commonly used in mathematics to simplify expressions and solve equations.


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To simplify, you write one copy of the base, then add the exponent. Example:x^5 times x^3 = x^8 In the case of positive integer exponents, this can easily be derived by writing each power as a repeated multiplication. However, this law is also valid for negative or fractional exponents.


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How do you use the integer rule to simplify expressions with positive and negative numbers?

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