Rules of Exponents

Front

What is the product of powers rule in exponents?

Back

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

Front

How do you simplify (c^5)(c^2)(c^2)?

Back

You add the exponents: c^(5+2+2) = c^9.

Front

What is the power of a power rule 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 (x^5)(x^5)?

Back

You add the exponents: x^(5+5) = x^10.

Front

What is the product of coefficients rule in multiplication of polynomials?

Back

When multiplying polynomials, multiply the coefficients and then apply the product of powers rule to the variables.

Front

How do you simplify (6x^2)(-3x^5)?

Back

Multiply the coefficients: 6 * -3 = -18, and add the exponents: x^(2+5) = x^7, so the answer is -18x^7.

Front

What is a negative exponent?

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 make a negative exponent positive?

Back

To make a negative exponent positive, take the reciprocal of the base. For example, 9^-3 = 1/9^3.

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

How do you simplify (5^4)^3?

Back

You multiply the exponents: 5^(4*3) = 5^12.