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

Calculate: (2x^5y^2/5)^3

Back

8x^15y^6/125.

Front

Calculate: (6x^(-1)y^3)^3

Back

216x^(-3)y^9.

Front

Calculate: 4x^(-2)y^3 * 3x^6y

Back

12x^4y^4.

Front

Calculate: (3x^2y^3/z^(-7))^3

Back

27x^6y^9z^(21).