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 × 2 × 2.

Front

What does x^0 equal?

Back

Any non-zero number raised to the power of 0 equals 1. So, x^0 = 1.

Front

How do you simplify x^a / x^b?

Back

To simplify x^a / x^b, subtract the exponents: x^(a-b).

Front

What is the product of powers property?

Back

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

Front

What is the quotient of powers property?

Back

When dividing powers with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

What is the power of a power property?

Back

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

Front

What is the power of a product property?

Back

When raising a product to a power, apply the exponent to each factor: (ab)^n = a^n * b^n.

Front

What is the power of a quotient property?

Back

When raising a quotient to a power, apply the exponent to both the numerator and the denominator: (a/b)^n = a^n / b^n.

Front

Simplify: (3^2)^3

Back

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

Front

Simplify: 2^3 × 2^4

Back

Using the product of powers property: 2^3 × 2^4 = 2^(3+4) = 2^7.