Question

which of the following expressions equal 1? select all that apply. (2 points)
□ 67¹ □ w⁹ □ x⁰ □ 6⁰
simplify the expression. write your answer as a fraction. (1 point)
8⁻² = □

Explanation:

Part 1: Which expressions equal 1?

• For \(67^1\): By the rule of exponents, any number to the power of 1 is the number itself, so \(67^1 = 67

eq1\).

• For \(w^9\): There's no general rule that \(w^9 = 1\) unless \(w = 1\) or \(w=- 1\) (but this isn't a general case), so \(w^9\) is not necessarily 1.
• For \(x^0\): By the zero - exponent rule, any non - zero number \(x\) raised to the power of 0 is 1, i.e., \(x^0=1\) (\(x

eq0\)).

• For \(6^0\): Using the zero - exponent rule, \(a^0 = 1\) for \(a

eq0\). Here \(a = 6
eq0\), so \(6^0=1\).

Step 1: Recall the negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for \(a
eq0\) and \(n\) is a positive integer. Here \(a = 8\) and \(n = 2\).

Step 2: Apply the rule

\(8^{-2}=\frac{1}{8^{2}}\)

Step 3: Calculate \(8^{2}\)

\(8^{2}=8\times8 = 64\)

Step 4: Substitute back

\(8^{-2}=\frac{1}{64}\)

Answer:

\(x^0\), \(6^0\)

Part 2: Simplify \(8^{-2}\)