5.0 Negative Exponents and Zero Power

Front

What is a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal raised to the opposite positive exponent. For example, a^{-n} = 1/a^n.

Front

How do you rewrite a number with a negative exponent as a positive exponent?

Back

To rewrite a number with a negative exponent, take the reciprocal of the base and change the sign of the exponent. For example, 2w^{-3} = 1/(2w^3).

Front

What is the value of any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero is equal to 1. For example, 5^0 = 1.

Front

What is the result of simplifying x^0?

Back

The result of simplifying x^0 is 1, as long as x is not equal to zero.

Front

How do you simplify an expression with a negative exponent in the numerator?

Back

To simplify an expression with a negative exponent in the numerator, move the base to the denominator and change the sign of the exponent. For example, 2^{-3} = 1/(2^3).

Front

What is the rule for multiplying powers with the same base?

Back

When multiplying powers with the same base, add the exponents. For example, a^m * a^n = a^{m+n}.

Front

What is the rule for dividing powers with the same base?

Back

When dividing powers with the same base, subtract the exponents. For example, a^m / a^n = a^{m-n}.

Front

How do you simplify the expression (x^5)/(x^{-2})?

Back

To simplify (x^5)/(x^{-2}), subtract the exponents: x^{5 - (-2)} = x^{5 + 2} = x^7.

Front

What is the result of simplifying the expression -12(x^0)?

Back

The result of simplifying -12(x^0) is -12, since x^0 = 1.

Front

How do you handle negative exponents in a fraction?

Back

To handle negative exponents in a fraction, move the base with the negative exponent to the opposite part of the fraction (numerator to denominator or vice versa) and change the sign of the exponent.