Simplifying Exponents

Front

What is the definition of a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal and raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n).

Front

Simplify: a^(-3)

Back

1/(a^3)

Front

What is the rule for multiplying exponents with the same base?

Back

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

Front

Simplify: a^2 * a^3

Back

a^(2+3) = a^5

Front

What is the rule for dividing exponents with the same base?

Back

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

Front

Simplify: a^5 / a^2

Back

a^(5-2) = a^3

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).

Front

Simplify: (a^2)^3

Back

a^(2*3) = a^6

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

Simplify: a^0

Back

1