Question

directions: simplify. write answer in standard form.

1. $\frac{8^{9}}{8^{7}}$
2. $\frac{c^{22}}{c^{10}cdot c^{5}}$

Explanation:

Step1: Apply exponent - division rule

When dividing two powers with the same base \(a^m\div a^n=a^{m - n}\). For \(\frac{8^9}{8^7}\), here \(a = 8\), \(m = 9\), \(n = 7\), so \(\frac{8^9}{8^7}=8^{9 - 7}\).

Step2: Calculate the exponent value

\(9-7 = 2\), so \(8^{9 - 7}=8^2\).

Step3: Evaluate the power

\(8^2=8\times8 = 64\).

For \(\frac{c^{22}}{c^{10}\cdot c^{5}}\):

Step1: Apply exponent - multiplication rule

When multiplying two powers with the same base \(a^m\cdot a^n=a^{m + n}\). So \(c^{10}\cdot c^{5}=c^{10 + 5}=c^{15}\).

Step2: Apply exponent - division rule

Now we have \(\frac{c^{22}}{c^{15}}\), using \(a^m\div a^n=a^{m - n}\) with \(a = c\), \(m = 22\), \(n = 15\), we get \(\frac{c^{22}}{c^{15}}=c^{22-15}\).

Step3: Calculate the exponent value

\(22 - 15=7\), so \(c^{22-15}=c^7\).

Answer:

1. \(64\)
2. \(c^7\)