Properties of Exponents

Front

What is the product of powers property of exponents?

Back

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

Front

What is the power of a power property of exponents?

Back

When raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*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 the expression 3^4 ⋅ 3^7?

Back

Using the product of powers property, you add the exponents: 3^4 ⋅ 3^7 = 3^(4+7) = 3^11.

Front

What is the simplified form of (8^5)^3?

Back

Using the power of a power property, you multiply the exponents: (8^5)^3 = 8^(5*3) = 8^15.

Front

How do you simplify the expression 2x^0y^3?

Back

Using the zero exponent rule, x^0 = 1, so 2x^0y^3 simplifies to 2y^3.

Front

What is the simplified form of 6^(-4)?

Back

Using the negative exponent rule, 6^(-4) = 1/(6^4).

Front

What does (3x)^0 equal?

Back

According to the zero exponent rule, (3x)^0 = 1.

Front

What is the general form of the exponent rules?

Back

The exponent rules include: product of powers, power of a power, zero exponent, negative exponent, and quotient of powers.