Properties of Exponents Flashcard

Front

What is the product of powers rule in exponents?

Back

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

Front

What is the power of a power rule in exponents?

Back

When raising an exponential expression to another exponent, multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the quotient of powers rule in exponents?

Back

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

Front

What happens to the exponent when raising a product to a power?

Back

When raising a product to a power, distribute the exponent to each factor: (xy)^n = x^n * y^n.

Front

What happens to the exponent when raising a quotient to a power?

Back

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

Front

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

Back

x^4y^6.

Front

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

Back

6x^5.

Front

Simplify: x^5 / x^2

Back

x^3.

Front

What is the zero exponent rule?

Back

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

Front

What is the negative exponent rule?

Back

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