Properties of Exponents and Rational Exponents

Front

What is the property of exponents that states any number raised to the power of zero equals one?

Back

Anything raised to a power of zero is always 1.

Front

Simplify the expression: (6x^-1y^3)^3

Back

216x^-3y^9

Front

What is the definition of a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a root and a power.

Front

Convert the expression n^3/2 into a rational exponent form.

Back

n^{3/2}

Front

What is the result of x^m * x^n?

Back

x^{m+n} (Add the exponents)

Front

What is the result of (x^m)^n?

Back

x^{mn} (Multiply the exponents)

Front

What is the result of x^m / x^n?

Back

x^{m-n} (Subtract the exponents)

Front

What happens when you raise a product to a power?

Back

(ab)^n = a^n * b^n (Distribute the exponent)

Front

What happens when you raise a quotient to a power?

Back

(a/b)^n = a^n / b^n (Distribute the exponent)

Front

What is the value of 2^0?

Back

1 (Any non-zero number raised to the power of zero is 1)