Properties of Exponents

Front

What is the product of powers property of exponents?

Back

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

Front

What is the power of a power property of exponents?

Back

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

Front

What is the quotient of powers property of exponents?

Back

When dividing two powers with the same base, you subtract the exponents. For example, 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. 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 the expression (3x^2)(4x^3)?

Back

You multiply the coefficients and add the exponents: 12x^(2+3) = 12x^5.

Front

What happens when you divide x^5 by x^2?

Back

You subtract the exponents: x^(5-2) = x^3.

Front

What is the result of (2^3)^2?

Back

You multiply the exponents: 2^(3*2) = 2^6 = 64.

Front

How do you express 1/a^3 using positive exponents?

Back

1/a^3 = a^(-3).

Front

What is the simplified form of (x^4y^2)/(xy^3)?

Back

You subtract the exponents: x^(4-1)y^(2-3) = x^3y^(-1) = x^3/y.