Exponent Rules Flashcard

Front

What is the product of powers rule in exponentiation?

Back

When multiplying two expressions with the same base, you 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 quotient of powers rule in exponentiation?

Back

When dividing two expressions with the same base, you 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 the expression 4^2 * 4^3?

Back

Using the product of powers rule: 4^2 * 4^3 = 4^(2+3) = 4^5 = 1024.

Front

What is the value of (-4)^2?

Back

The value of (-4)^2 is 16, since squaring a negative number results in a positive number.

Front

How can you express 6^18 using the power of a power rule?

Back

6^18 can be expressed as (6^2)^9, since 2 * 9 = 18.

Front

What is the simplified form of 9x^16 / 3x^2?

Back

Using the quotient of powers rule: 9/3 = 3 and x^(16-2) = x^14, so the result is 3x^14.

Front

What is the value of 2^3?

Back

The value of 2^3 is 8, since 2 * 2 * 2 = 8.