Exponent Rules

Front

What is the product rule for exponents?

Back

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

Front

What is the quotient rule for exponents?

Back

When dividing two expressions with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

What happens when you raise a power to a power?

Back

When raising a power to another power, multiply the exponents: (a^m)^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

Simplify: (3x^4)(2x^2)

Back

6x^6.

Front

Simplify: (y^5)/(y^2)

Back

y^3.

Front

Rewrite using a positive exponent: z^(-4)

Back

1/(z^4).

Front

Simplify: (2a^3)(4a^5)

Back

8a^8.

Front

What is the rule for multiplying exponents with different bases?

Back

You cannot combine them; you must keep them separate: a^m * b^n remains as is.