Laws of Exponents

Front

What is the definition of a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal. For example, x^(-n) = 1/(x^n).

Front

What is the Power Rule of Exponents?

Back

The Power Rule states that (a^m)^n = a^(m*n).

Front

Simplify: x^3 * x^4

Back

x^(3+4) = x^7.

Front

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

Back

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

Front

What is the definition of a zero exponent?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1.

Front

Simplify: (x^5)/(x^2)

Back

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

Front

What is the definition of the Product of Powers property?

Back

The Product of Powers property states that a^m * a^n = a^(m+n).

Front

Simplify: (3x^2y^3)^2

Back

3^2 * (x^2)^2 * (y^3)^2 = 9x^4y^6.

Front

What is the definition of the Quotient of Powers property?

Back

The Quotient of Powers property states that a^m / a^n = a^(m-n).

Front

Simplify: (5^2)^3

Back

5^(2*3) = 5^6.