Question

ZWhich statements accurately describe the expression 6 · 6^0 · 6^–3? Select all that apply.

1.The 6 without an exponent is equivalent to the 6 having a 0 exponent.
2.The sum of the exponents is 2.
3.Multiplying the exponents simplifies the expression.
4.The expression has a value of 1/36.
5.An equivalent expression is 6^5 · 6^-7.

Answer 1

The expression 6 · 6^0 · 6^–3 can be simplified step-by-step by applying the rules of exponents. The value of the expression is 1/36.

Step-by-step explanation:

The expression 6 · 6^0 · 6^–3 can be simplified step-by-step:

1. Any number raised to the power of 0 is equal to 1. Therefore, 6^0 = 1.
2. Any number raised to a negative power can be written as the reciprocal of that number raised to the positive power. Therefore, 6^–3 = 1/6^3 = 1/216.
3. Multiplying the expression together, we get 6 · 1 · (1/216) = 6/216 = 1/36.

Therefore, the statements that accurately describe the expression are:

• 1. The 6 without an exponent is equivalent to the 6 having a 0 exponent.
• 4. The expression has a value of 1/36.