Properties of Exponents Review

Front

What is the product of powers property of exponents?

Back

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

Front

What is the power of a power property of exponents?

Back

The power of a power property 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 property of exponents?

Back

The power of a product property 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 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), where a ≠ 0.

Front

How do you simplify the expression 2^3 * 2^4?

Back

Using the product of powers property, you add the exponents: 2^3 * 2^4 = 2^(3+4) = 2^7.

Front

How do you simplify the expression (x^2)^3?

Back

Using the power of a power property, you multiply the exponents: (x^2)^3 = x^(2*3) = x^6.

Front

What is the result of (3xy)^2?

Back

Using the power of a product property, you distribute the exponent: (3xy)^2 = 3^2 * x^2 * y^2 = 9x^2y^2.

Front

What is the value of 5^0?

Back

According to the zero exponent rule, 5^0 = 1.

Front

What is the value of a^(-2)?

Back

Using the negative exponent rule, a^(-2) = 1/(a^2), where a ≠ 0.