Negative Exponents

Front

What is a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal and raised to the absolute value of the 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 as a positive exponent, take the reciprocal of the base and change the sign of the exponent. For example, x^(-m) = 1/(x^m).

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 an expression with a negative exponent?

Back

To simplify an expression with a negative exponent, rewrite it as a fraction with a positive exponent. For example, 5^(-2) = 1/(5^2).

Front

What happens when you raise a power to another power?

Back

When raising a power to another power, multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

How do you express a fraction with a negative exponent?

Back

A fraction with a negative exponent can be expressed as the reciprocal of the base raised to the positive exponent. For example, 1/(b^m) = b^(-m).

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, a^0 = 1 (where a ≠ 0).

Front

How do you convert a positive exponent to a negative exponent?

Back

To convert a positive exponent to a negative exponent, take the reciprocal of the base. For example, a^m = 1/(a^(-m)).

Front

What is the significance of negative exponents in scientific notation?

Back

Negative exponents in scientific notation indicate that the number is less than one and represents a decimal. For example, 3.0 x 10^(-2) = 0.03.