Laws of Exponents

Front

What is the Quotient Rule for exponents?

Back

The Quotient Rule states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

Evaluate: 3^5 / 3^2

Back

3^(5-2) = 3^3 = 27.

Front

What happens to an exponent when raising a power to another power?

Back

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

Front

Simplify: (x^3)^4

Back

x^(3*4) = x^12.

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

Evaluate: 7^0

Back

7^0 = 1.

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.

Front

Simplify: x^(-2)

Back

x^(-2) = 1/x^2.

Front

What is the Product Rule for exponents?

Back

The Product Rule states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

Evaluate: 2^3 * 2^4

Back

2^(3+4) = 2^7 = 128.