Identify the base of the multiplication.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for problems 6 and 7:

6. Express in power form: $\frac{5}{7} \times \frac{5}{7} \times \frac{5}{7} \times \frac{5}{7} \times \frac{5}{7}$

Identify the base of the multiplication.
The base is $\frac{5}{7}$ .
Count how many times the base is multiplied by itself.
The base $\frac{5}{7}$ is multiplied by itself 5 times.
Write the expression in power form.
$\left(\frac{5}{7}\right)^5$
The expression in power form is:
$\boxed{\left(\frac{5}{7}\right)^5}$
7. Evaluate: $\left(\frac{3}{11}\right)^{-1} \times \left(\frac{3}{11}\right)^2 \times \left(\frac{3}{11}\right)^3 \times \left(\frac{3}{11}\right)^{-4}$
Identify the common base.
The common base is $\frac{3}{11}$ .
Apply the exponent rule $a^m \times a^n = a^{m+n}$ to combine the terms.
Add all the exponents:
$-1 + 2 + 3 + (-4)$
Calculate the sum of the exponents.
$-1 + 2 + 3 - 4 = 1 + 3 - 4 = 4 - 4 = 0$
Substitute the sum of the exponents back into the expression.
$\left(\frac{3}{11}\right)^0$
Evaluate the expression.
Any non-zero number raised to the power of 0 is 1.
$\left(\frac{3}{11}\right)^0 = 1$
The evaluated expression is:
$\boxed{1}$

Answer