Negative Exponents with variables

Front

What is an exponent?

Back

An exponent is a mathematical notation indicating the number of times a number (the base) is multiplied by itself.

Front

What does a negative exponent represent?

Back

A negative exponent represents the reciprocal of the base raised to the absolute value of the exponent. For example, x^{-n} = 1/x^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 the base in the denominator and the exponent made positive.

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

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero equals one. For example, a^0 = 1.

Front

How do you express a variable with a negative exponent in positive form?

Back

To express a variable with a negative exponent in positive form, move it to the opposite side of the fraction. For example, x^{-1} = 1/x.

Front

What is the simplified form of x^{-2}y^3?

Back

The simplified form is y^3 / x^2.

Front

What is the simplified form of a^{-3}b^2?

Back

The simplified form is b^2 / a^3.

Front

How do you simplify the expression a^2 / b^{-3}c^{-4}?

Back

The simplified form is a^2 * b^3 * c^4.