Question

correction 1.4
selected response: 1 point for correct answe
simplify: $7a^{-3}b^{3}$
$7ab^{6}$
$7a^{3}b^{-3}$
$\frac{b^{3}}{7a^{3}}$
$\frac{7b^{3}}{a^{3}}$

Explanation:

Step1: Recall the negative exponent rule

The negative exponent rule states that \( a^{-n}=\frac{1}{a^{n}} \) (where \( a
eq0 \) and \( n \) is a positive integer). So for \( 7a^{-3}b^{3} \), we can apply this rule to the term with the negative exponent.

Step2: Apply the negative exponent rule to \( a^{-3} \)

Using \( a^{-n}=\frac{1}{a^{n}} \), we have \( a^{-3}=\frac{1}{a^{3}} \). Substituting this back into the expression \( 7a^{-3}b^{3} \), we get \( 7\times\frac{1}{a^{3}}\times b^{3} \).

Step3: Simplify the expression

Multiplying the terms together, we have \( \frac{7b^{3}}{a^{3}} \).

Answer:

\(\frac{7b^{3}}{a^{3}}\) (corresponding to the option \(\frac{7b^{3}}{a^{3}}\) in the given choices)