Exponent Rules

Front

What is the product of powers rule in exponentiation?

Back

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

Front

What is the power of a power rule in exponentiation?

Back

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

Front

What is the power of a product rule in exponentiation?

Back

When raising a product to a power, apply the exponent to each factor: (ab)^n = a^n * b^n.

Front

What is the zero exponent rule?

Back

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

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Front

How do you simplify x^5 * x^3?

Back

Using the product of powers rule: x^5 * x^3 = x^(5+3) = x^8.

Front

What is the base in an exponential expression?

Back

The base is the number that is raised to a power in an exponential expression, e.g., in 2^7, the base is 2.

Front

What is the result of (-4x)^0?

Back

According to the zero exponent rule, (-4x)^0 = 1.

Front

How do you simplify (a^3b^5)^7?

Back

Using the power of a product rule: (a^3b^5)^7 = a^(3*7) * b^(5*7) = a^21 * b^35.

Front

What is the quotient of powers rule in exponentiation?

Back

When dividing two expressions with the same base, subtract the exponents: a^m / a^n = a^(m-n).