Laws of Exponents

Front

What is the product of powers property in exponents?

Back

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

Front

What is the power of a power property in exponents?

Back

When raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the power of a product property in exponents?

Back

When raising a product to a power, you distribute the exponent to each factor: (ab)^n = a^n * b^n.

Front

What is the power of a quotient property in exponents?

Back

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

Front

What is the zero exponent rule?

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 rule?

Back

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

Front

How do you simplify the expression (7^2m^9n^3)^7?

Back

Using the power of a power property, you multiply the exponents: 7^(2*7)m^(9*7)n^(3*7) = 7^14m^63n^21.

Front

How do you simplify the expression 2^4x^2x^3x^4?

Back

Combine the exponents of x: 2^4 * x^(2+3+4) = 2^4 * x^9.

Front

How do you simplify the expression (xy^2/y)^6?

Back

First simplify the fraction: (x * y^(2-1))^6 = (xy)^6 = x^6y^6.

Front

How do you simplify the expression (8k^2/k^3)^2?

Back

First simplify the fraction: (8/k)^(2) * (k^2/k^3)^(2) = 8^2/k^2.