Question

multiply & divide powers (integer exponents)
google classroom microsoft teams
simplify.
rewrite the expression in the form z^n.
\\(\frac{z^7}{z^{-14}} = \\)

Explanation:

Step1: Recall exponent rule for division

When dividing powers with the same base, we use the rule \( \frac{a^m}{a^n}=a^{m - n} \). Here, the base is \( z \), \( m = 7 \), and \( n=- 14 \).

Step2: Apply the exponent rule

Substitute the values into the rule: \( \frac{z^{7}}{z^{-14}}=z^{7-(-14)} \).

Step3: Simplify the exponent

Simplify \( 7-(-14) \). Subtracting a negative is like adding the positive, so \( 7 + 14=21 \). Thus, the expression becomes \( z^{21} \).

Answer:

\( z^{21} \)