Properties of Exponents

Front

What is the product of powers property of exponents?

Back

When multiplying two powers with the same base, 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, 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, apply 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, apply the exponent to both the numerator and the denominator: (a/b)^n = a^n / b^n.

Front

What is the zero exponent property?

Back

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

Front

What is the negative exponent property?

Back

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

Front

Simplify: (12x^3y)^2

Back

144x^6y^2.

Front

Simplify: (2a^2b^4z)(6a^3b^2z^5)

Back

12a^5b^6z^6.

Front

Simplify: \frac{x^{-7}}{x^4}

Back

\frac{1}{x^{11}}.

Front

Simplify: \frac{(2x^4y^4)(2x^3y)}{3y^2}

Back

\frac{4x^7y^3}{3}.