Exponent Properties

Front

What is the power of a power property in exponents?

Back

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

Front

How do you simplify (2^8)^2?

Back

Using the power of a power property, (2^8)^2 = 2^(8*2) = 2^16.

Front

What is the product of powers property in exponents?

Back

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

Front

How do you simplify 7^2 * 7^3?

Back

Using the product of powers property, 7^2 * 7^3 = 7^(2+3) = 7^5.

Front

What is the quotient of powers property in exponents?

Back

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

Front

How do you evaluate 81^5 using the quotient of powers rule?

Back

First, express 81 as 9^2. Then, (9^2)^5 = 9^(2*5) = 9^10.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one. For example, 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. For example, a^(-n) = 1/(a^n).

Front

How do you simplify 3^10 / 3^5?

Back

Using the quotient of powers property, 3^10 / 3^5 = 3^(10-5) = 3^5.

Front

What is the power of a product property in exponents?

Back

When raising a product to a power, you raise each factor to that power. For example, (ab)^n = a^n * b^n.