Exponent Rules and Applications

Front

What is the Quotient Rule for exponents?

Back

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

Front

Evaluate: 9^5 / 9^0

Back

9^5 (since any number to the power of 0 is 1).

Front

What happens when you raise a power to a power?

Back

You multiply the exponents: (a^m)^n = a^(m*n).

Front

Make the exponent positive: 9^-3

Back

1/9^3 (negative exponents indicate reciprocal).

Front

Simplify: (n^2)(n^4)(n^5)

Back

n^(2+4+5) = n^11 (add the exponents).

Front

What is the value of any non-zero number raised to the power of 0?

Back

1 (a^0 = 1 for a ≠ 0).

Front

Evaluate: 2^3 * 2^2

Back

2^(3+2) = 2^5 = 32 (add the exponents).

Front

What is the Product Rule for exponents?

Back

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

Front

Simplify: (3^2)^3

Back

3^(2*3) = 3^6 = 729 (multiply the exponents).

Front

Evaluate: 5^4 / 5^2

Back

5^(4-2) = 5^2 = 25 (subtract the exponents).