Properties of Exponents

Front

What is the product of powers property of exponents?

Back

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

Front

How do you simplify (xy)^7?

Back

(xy)^7 = x^7 * y^7.

Front

What is the result of (x^5)(x^4)?

Back

The result is x^(5+4) = x^9.

Front

What is the coefficient when multiplying (3x^4)(6x^6)?

Back

The coefficient is 3 * 6 = 18, and the variable part is x^(4+6) = x^10, so the result is 18x^10.

Front

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

Back

You add the exponents: x^(2+2+2+2) = x^8.

Front

What is the power of a power property of exponents?

Back

When raising a power to another power, you multiply the exponents: (a^m)^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: a^(-n) = 1/(a^n).

Front

How do you simplify (2x^3)^2?

Back

You apply the power of a power property: (2^2)(x^(3*2)) = 4x^6.

Front

What is the quotient of powers property of exponents?

Back

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