Exponent Product Rule

Front

What is the Exponent Product Rule?

Back

The Exponent Product Rule states that when multiplying two expressions with the same base, you can add their exponents: a^m * a^n = a^(m+n).

Front

Simplify: (x^3)(x^5)

Back

x^(3+5) = x^8.

Front

What happens to the exponents when multiplying two powers with the same base?

Back

You add the exponents.

Front

Simplify: (2^4)(2^2)

Back

2^(4+2) = 2^6 = 64.

Front

If a^m * a^n = a^p, what is the relationship between m, n, and p?

Back

p = m + n.

Front

Simplify: (-3)^2 * (-3)^4

Back

(-3)^(2+4) = (-3)^6.

Front

What is the result of multiplying two negative bases with exponents?

Back

The result depends on the sum of the exponents; if the sum is even, the result is positive; if odd, the result is negative.

Front

Simplify: (a^2b^3)(a^3b^2)

Back

a^(2+3)b^(3+2) = a^5b^5.

Front

What is the Exponent Zero Rule?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1.

Front

Simplify: (y^{-3})(y^5)

Back

y^(-3+5) = y^2.