Question

1. ((x^{-3})(x^{-3}) =)

a (x^6)
b (x^9)
c (\frac{1}{x^6})
d (\frac{1}{x^9})

Explanation:

Step1: Recall the exponent rule for multiplication

When multiplying two exponential expressions with the same base, we add the exponents. The formula is \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(x\), and both exponents are \(-3\). So, \((x^{-3})(x^{-3}) = x^{-3 + (-3)}\).

Step2: Simplify the exponent

Calculate \(-3 + (-3)\), which equals \(-6\). So now we have \(x^{-6}\).

Step3: Recall the negative exponent rule

A negative exponent means the reciprocal of the positive exponent. The formula is \(a^{-n}=\frac{1}{a^n}\). Applying this to \(x^{-6}\), we get \(\frac{1}{x^6}\).

Answer:

C. \(\frac{1}{x^6}\)