Does a negative exponent result in a negative answer?

Asked by: Eric Stoehr

Negative numbers give a negative result when their exponent is odd and they give a positive result when the exponent is even. For example, (-5)³ = -125, (-5)⁴ = 625. A positive number with a negative exponent will always give a positive number. For example, 2^–3 = 1/8, which is a positive number.

What are the rules for negative exponents?

The law of negative exponents states that, when a number is raised to a negative exponent, we divide 1 by the base raised to a positive exponent. The general formula of this rule is: a ^–m = 1/a ^m and (a/b) ^–n = (b/a) ⁿ.

What does a negative exponent mean?

As the page explains, a negative exponent just means “the multiplicative inverse of the base raised to the positive opposite of the power“. So a^(-b) = 1/(a^b). The base, a, doesn’t change.

How do you solve a problem with a negative exponent?

So this 3 with a negative 2 exponent in the denominator is a 3 with a positive 2 exponent in the numerator. And we can't forget about this one which is also in the numerator as well.

How do negative exponents become positive?

Numbers okay. So if we've also got 3 to the second power over 3 to the second power because the numerator and denominator are the same they're going to equal 1 won't they. And if we've got xy to the

What is 5 with a negative 2 exponent?

0.04

Answer: 5 to the power of negative 2 is 0.04.

What is 10 to the negative power of 3?

0.001

Answer: 10 to the power of negative 3 is 0.001.

What is 10 to the negative power of 2?

0.01

Answer: The value of 10 to the power of negative 2 is 0.01.

What are the rules of exponents?

The exponent rules are:

• Product of powers rule — Add powers together when multiplying like bases.
• Quotient of powers rule — Subtract powers when dividing like bases.
• Power of powers rule — Multiply powers together when raising a power by another exponent.

Why are negative exponents reciprocals?

First thing you need to remember is that what a negative exponent does is it takes the reciprocal of the base. So 5 to the negative 2 is the same as 1 over 5 all to the positive 2 so it takes the

What are laws of exponents?

Definition of law of exponents



: one of a set of rules in algebra: exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent: a^m×aⁿ=a^m+n; a^m÷aⁿ=a^m−n; (a^m)ⁿ=a^mn.

What are the 7 rules of exponents with examples?

7 Rules for Exponents with Examples

• RULE 1: Zero Property. Definition: Any nonzero real number raised to the power of zero will be 1. …
• RULE 2: Negative Property. …
• RULE 3: Product Property. …
• RULE 4: Quotient Property. …
• RULE 5: Power of a Power Property. …
• RULE 6: Power of a Product Property. …
• RULE 7: Power of a Quotient Property.

What are the 8 rules of exponents?

Rules of Exponents With Examples

• a^m×aⁿ = a. ^m+n
• a^m/aⁿ = a. ^m-n
• (a^m)ⁿ = a. ^mn
• aⁿ/bⁿ = (a/b) ⁿ
• a⁰ = 1.
• a^–m = 1/a. ^m
• a 1 n = a n.