Product Rule and Negative Exponents

Front

What is the Product Rule in exponentiation?

Back

The 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

How do you simplify x^{-9} * x^5?

Back

Using the Product Rule, x^{-9} * x^5 = x^{-9+5} = x^{-4} = 1/x^4.

Front

What is the value of an exponent when a number or variable does not have one?

Back

The exponent is assumed to be 1.

Front

What is the base in the expression 4^3?

Back

The base is 4.

Front

How do you simplify a^2 * a^4 using the Product Rule?

Back

Using the Product Rule, a^2 * a^4 = a^(2+4) = a^6.

Front

What is the definition of a negative exponent?

Back

A negative exponent indicates that the base should be taken as the reciprocal: a^{-n} = 1/a^n.

Front

How do you express 1/x^4 using positive exponents?

Back

1/x^4 can be expressed as x^{-4}.

Front

What is the result of multiplying two powers with different bases?

Back

You cannot combine them using the Product Rule; you must leave them as separate terms.

Front

What is the simplified form of 23^29?

Back

23^29 is already in its simplest exponential form.

Front

How do you convert a negative exponent into a positive exponent?

Back

To convert a negative exponent to a positive exponent, take the reciprocal of the base: a^{-n} = 1/a^n.