Laws of Exponents

Front

What is the Product of Powers Rule in exponents?

Back

The Product of Powers Rule states that when multiplying two expressions with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

What is the Quotient of Powers Rule in exponents?

Back

The Quotient of Powers Rule states that when dividing two expressions with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Front

What is the Power of a Power Rule in exponents?

Back

The Power of a Power Rule states that when raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

What is the Power of a Product Rule in exponents?

Back

The Power of a Product Rule states that when raising a product to a power, you can distribute the exponent to each factor. For example, (ab)^n = a^n * b^n.

Front

What is the Power of a Quotient Rule in exponents?

Back

The Power of a Quotient Rule states that when raising a quotient to a power, you can distribute the exponent to the numerator and denominator. For example, (a/b)^n = a^n / b^n.

Front

What is the Zero Exponent Rule?

Back

The Zero Exponent Rule states that any non-zero base raised to the power of zero equals one. For example, a^0 = 1, where a ≠ 0.

Front

What is the Negative Exponent Rule?

Back

The Negative Exponent Rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/a^n.

Front

How do you simplify expressions with fractional exponents?

Back

Fractional exponents represent roots. For example, a^(1/n) is the nth root of a, and a^(m/n) is the nth root of a raised to the mth power.

Front

What is the significance of the base in exponentiation?

Back

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

Front

What is the relationship between exponents and logarithms?

Back

Exponents and logarithms are inverse operations. If b^y = x, then log_b(x) = y.