Properties of Exponents and Rational Exponents

Front

What is the product of powers property of exponents?

Back

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

Front

What is the power of a power property of exponents?

Back

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

Front

What is the power of a product property of exponents?

Back

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

Front

What is the power of a quotient property of exponents?

Back

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

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero is equal to one: a^0 = 1.

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/a^n.

Front

How do you simplify (3x^3y^5)^4?

Back

You apply the power of a product property: (3^4)(x^(3*4))(y^(5*4)) = 81x^12y^20.

Front

What is the definition of rational exponents?

Back

Rational exponents represent roots: a^(m/n) = n√(a^m).

Front

What is the relationship between exponents and roots?

Back

Exponents can be expressed as roots: a^(1/n) = n√a.

Front

How do you simplify x^0?

Back

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