Exponents & Exponent Properties

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 property?

Back

When multiplying powers 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 property?

Back

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

Front

What is the quotient of powers property?

Back

When dividing powers with the same base, you subtract the exponents. For example, a^m ÷ a^n = a^(m-n).

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero equals one. For example, 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. For example, a^(-n) = 1/(a^n).

Front

Simplify: (3^2) × (3^3)

Back

3^(2+3) = 3^5 = 243.

Front

Simplify: (x^4) ÷ (x^2)

Back

x^(4-2) = x^2.

Front

Write with positive exponents: 1/(b^(-3))

Back

b^3.

Front

What happens when you multiply powers with different bases?

Back

You cannot combine them using exponents; you simply multiply the bases. For example, a^m × b^n remains as is.