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 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.

Front

What is the negative exponent property?

Back

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

Front

Calculate (2^3)^2.

Back

2^(3*2) = 2^6 = 64.

Front

Simplify x^5 * x^4.

Back

x^(5+4) = x^9.

Front

Calculate (3x^2y)^3.

Back

27x^(2*3)y^3 = 27x^6y^3.

Front

Rewrite 5y^(-2) using a positive exponent.

Back

5/y^2.