Exponential Rules (warmup for 4.1)

Front

What is the quotient rule for exponents?

Back

When dividing two expressions with the same base, subtract the exponent of the denominator from the exponent of the numerator: a^m / a^n = a^(m-n).

Front

How do you simplify a negative exponent?

Back

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

Front

What is the value of any non-zero number raised to the zero power?

Back

Any non-zero number raised to the zero power is equal to 1: a^0 = 1 (where a ≠ 0).

Front

What happens to the exponents when multiplying two expressions with the same base?

Back

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

Front

What is the simplified form of 4^(-2)?

Back

4^(-2) simplifies to 1/16.

Front

If a^m = a^n, what can we conclude about m and n?

Back

If a^m = a^n, then m must equal n, provided that a is not zero.

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

How do you express 134^0 in simplified form?

Back

134^0 simplifies to 1.

Front

What is the relationship between exponents and roots?

Back

The exponent can be expressed as a root: a^(1/n) = n√a.

Front

What is the power of a power rule?

Back

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