Properties of Exponents

Front

What is the product of powers property?

Back

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

Front

What is the power of a power property?

Back

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

Front

What is the power of a product property?

Back

When raising a product to a power, apply the exponent to each factor: (ab)^n = a^n * b^n.

Front

What is the power of a quotient property?

Back

When raising a quotient to a power, apply the exponent to both the numerator and denominator: (a/b)^n = a^n / b^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

Calculate (2^3)^2.

Back

2^(3*2) = 2^6 = 64.

Front

Calculate 5^3 * 5^2.

Back

5^(3+2) = 5^5 = 3125.

Front

Which is larger: 4^3 or 3^4?

Back

4^3 = 64 and 3^4 = 81, so 3^4 is larger.

Front

Evaluate -2^4.

Back

-2^4 = -16 (the negative sign is not included in the exponent).