6.2 Exponents - Product/Zero/Negatives

Front

What is the product of two powers with the same base?

Back

To multiply two powers with the same base, add their exponents. For example, a^m * a^n = a^(m+n).

Front

What is the value of any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero is equal to 1. For example, 5^0 = 1.

Front

What does a negative exponent represent?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, a^-n = 1/a^n.

Front

Simplify the expression: (2a^2b^4z)(6a^3b^2z^5)

Back

12a^5b^6z^6.

Front

Simplify x^-7.

Back

1/x^7.

Front

Simplify the expression: 3x^2⋅x^2.

Back

3x^4.

Front

Simplify the expression: 5a^3b^5⋅3a^2b^2.

Back

15a^5b^7.

Front

Simplify the expression: (6x^2)(-3x^5).

Back

-18x^7.

Front

What is the rule for multiplying powers with different bases?

Back

When multiplying powers with different bases, you cannot combine the bases, but you can multiply the coefficients. For example, 2^3 * 3^2 = 8 * 9 = 72.

Front

What is the rule for dividing powers with the same base?

Back

To divide powers with the same base, subtract the exponents. For example, a^m / a^n = a^(m-n).