Laws of Exponents

Front

What is the Law of Exponents?

Back

The Law of Exponents refers to the rules that govern how to handle mathematical operations involving exponents, such as multiplication, division, and raising powers.

Front

What does it mean when a base has an exponent of 0?

Back

Any non-zero base raised to the power of 0 equals 1. For example, x^0 = 1 (where x ≠ 0).

Front

What is the Product Rule of Exponents?

Back

The Product Rule states that when multiplying two powers with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

What is the Quotient Rule of Exponents?

Back

The Quotient Rule states that when dividing two powers with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Front

What happens when you raise a power to another power?

Back

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

Front

What is the value of any number raised to the power of 1?

Back

Any number raised to the power of 1 is the number itself. For example, a^1 = a.

Front

What is the value of 0 raised to any positive exponent?

Back

0 raised to any positive exponent is 0. For example, 0^n = 0 (where n > 0).

Front

What is the value of 1 raised to any exponent?

Back

1 raised to any exponent is always 1. For example, 1^n = 1 for any integer n.

Front

Simplify: (x^3 * x^2).

Back

Using the Product Rule, x^3 * x^2 = x^(3+2) = x^5.

Front

Simplify: (2^4) * (2^3).

Back

Using the Product Rule, 2^4 * 2^3 = 2^(4+3) = 2^7.