Laws of Exponents

Front

What is the Quotient Rule of Exponents?

Back

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

Front

Evaluate: 3^4 / 3^2

Back

3^(4-2) = 3^2 = 9.

Front

What happens when you raise a power to a power?

Back

Multiply the exponents: (a^m)^n = a^(m*n).

Front

Evaluate: (y^9)^-2

Back

y^(9*-2) = y^-18 = 1/y^18.

Front

What is the Zero Exponent Rule?

Back

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

Front

Evaluate: (5^3 * x^2 * y^4)^0

Back

= 1 (since anything to the power of 0 is 1).

Front

What is the Product Rule of Exponents?

Back

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

Front

Evaluate: 9^5 * 9^9

Back

9^(5+9) = 9^14.

Front

Simplify: (x^2y)^5

Back

= x^(2*5) * y^5 = x^10y^5.

Front

What is the Negative Exponent Rule?

Back

A negative exponent indicates the reciprocal: a^-n = 1/a^n.