Simplifying Exponent Expressions (Laws of Exponents)

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 × 2 × 2 = 8).

Front

What is the product of powers rule?

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 power of a power rule?

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?

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 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

Simplify: 3^4 × 3^2

Back

Using the product of powers rule: 3^(4+2) = 3^6 = 729.

Front

Simplify: (2^3)^2

Back

Using the power of a power rule: 2^(3*2) = 2^6 = 64.

Front

Simplify: (xy)^3

Back

Using the power of a product rule: x^3 * y^3.

Front

What is the value of 5^0?

Back

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