Exponent Rules

Front

What is the power of a product rule in exponentiation?

Back

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

Front

What is the power of a power rule in exponentiation?

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 quotient rule in exponentiation?

Back

When dividing two bases with the same exponent, you can subtract the exponents: a^m / a^n = a^(m-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 (4xy^3)^3?

Back

Apply the power of a product rule: (4^3)(x^3)(y^(3*3)) = 64x^3y^9.

Front

How do you simplify 7x^0 * 5x^3?

Back

Since x^0 = 1, it simplifies to 7 * 1 * 5x^3 = 35x^3.

Front

What is the result of 3x^2 / 7x^2?

Back

Since the x^2 terms cancel out, the result is 3/7.

Front

How do you simplify x^5?

Back

x^5 is already in its simplest form.

Front

How do you simplify -48c^2d^4 / 8cd?

Back

Divide coefficients and subtract exponents: -6c^(2-1)d^(4-1) = -6cd^3.