Laws of Exponents

Front

What is the product of powers rule in exponents?

Back

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

Front

What is the power of a product rule in 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 rule in 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 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 (x^2y)^5?

Back

Use the power of a product rule: (x^2y)^5 = x^(2*5)y^5 = x^10y^5.

Front

How do you simplify (2ab)^3?

Back

Use the power of a product rule: (2ab)^3 = 2^3 * a^3 * b^3 = 8a^3b^3.

Front

How do you convert 9^(-3) to a positive exponent?

Back

Use the negative exponent rule: 9^(-3) = 1/9^3.

Front

What is the result of multiplying (-4r^5)(2r^8)?

Back

Combine coefficients and add exponents: (-4*2)(r^(5+8)) = -8r^13.