Exponent Rules

Front

What are the basic exponent rules?

Back

1. Product of Powers: a^m * a^n = a^(m+n) 2. Quotient of Powers: a^m / a^n = a^(m-n) 3. Power of a Power: (a^m)^n = a^(m*n) 4. Power of a Product: (ab)^n = a^n * b^n 5. Power of a Quotient: (a/b)^n = a^n / b^n 6. Zero Exponent: a^0 = 1 (a ≠ 0) 7. Negative Exponent: a^(-n) = 1/a^n.

Front

How do you combine like terms in algebraic expressions?

Back

To combine like terms, identify terms that have the same variable raised to the same power and add or subtract their coefficients.

Front

What is the result of (x^14)^3?

Back

The result is x^(14*3) = x^42.

Front

What is the simplified form of b^6 / 2a^2?

Back

The expression is already simplified as b^6 / 2a^2.

Front

How do you simplify the expression 8x^6y^12?

Back

The expression is already in its simplest form.

Front

What is the Product of Powers rule?

Back

The Product of Powers rule states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the Quotient of Powers rule?

Back

The Quotient of Powers rule states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

What does a^0 equal?

Back

a^0 equals 1, provided that a is not equal to 0.

Front

What is the Power of a Power rule?

Back

The Power of a Power rule states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

How do you simplify (2x^3)(3x^4)?

Back

You multiply the coefficients and add the exponents: (2*3)(x^(3+4)) = 6x^7.