Rules of Exponents

Front

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

Back

When dividing exponents with the same base, subtract the exponent in the denominator from the exponent in the numerator: a^m / a^n = a^(m-n).

Front

How do you simplify an expression with a base raised to the power of zero?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What is the product of powers rule?

Back

When multiplying exponents with the same base, add the exponents: a^m * a^n = a^(m+n).

Front

How do you simplify the expression (c^5)(c^2)(c^2)?

Back

Using the product of powers rule, add the exponents: c^5 * c^2 * c^2 = c^(5+2+2) = c^9.

Front

What is the rule for raising a power to another power?

Back

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

Front

What happens when you raise a fraction to a power?

Back

When raising a fraction to a power, raise both the numerator and the denominator to that power: (a/b)^n = a^n / b^n.

Front

What is the rule for negative exponents?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/a^n.

Front

How do you simplify the expression m^12 / m^3?

Back

Using the quotient of powers rule, subtract the exponents: m^12 / m^3 = m^(12-3) = m^9.

Front

What is the value of (-1/2)^0?

Back

Any non-zero number raised to the power of zero equals one: (-1/2)^0 = 1.

Front

What is the significance of the base in exponentiation?

Back

The base is the number that is being multiplied by itself, and the exponent indicates how many times the base is used as a factor.