Laws of Exponents

Front

What is the law of exponents for multiplying expressions with the same base?

Back

When multiplying expressions with the same base, add the exponents. For example, a^m * a^n = a^(m+n).

Front

What is the law of exponents for dividing expressions with the same base?

Back

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

Front

What happens when an exponent is zero?

Back

Any non-zero number raised to the power of zero is equal to 1. For example, 5^0 = 1.

Front

What is the law of exponents for raising a power to another power?

Back

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

Front

Simplify: (3x^2)^4

Back

3^4 * x^(2*4) = 81x^8.

Front

What is the law of exponents for raising a product to a power?

Back

When raising a product to a power, raise each factor to the power. For example, (ab)^n = a^n * b^n.

Front

Simplify: (2xy)^3

Back

2^3 * x^3 * y^3 = 8x^3y^3.

Front

What is the law of exponents for negative exponents?

Back

A negative exponent indicates the reciprocal. For example, a^(-n) = 1/(a^n).

Front

Simplify: x^3 / x^5

Back

x^(3-5) = x^(-2) = 1/(x^2).

Front

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

Back

0 raised to any positive exponent is 0. For example, 0^3 = 0.