Simplify (6×3)^7 ÷ (3×6)^2: Advanced Exponent Division

Question

Insert the corresponding expression:

$\frac{\left(6\times3\right)^7}{\left(3\times6\right)^2}=$

00:00 Simply

00:03 In multiplication, the order of factors doesn't matter

00:08 We'll use this formula in our exercise and reverse the order of factors

00:13 We'll use the formula for dividing powers

00:16 Any number (A) to the power of (N) divided by the same base (A) to the power of (M)

00:19 equals the number (A) to the power of the difference of exponents (M-N)

00:22 We'll use this formula in our exercise

00:26 Let's calculate the power

00:31 Let's switch back the order of factors

00:35 And this is the solution to the question

Let's solve the expression step-by-step using the power of a quotient rule for exponents.

The provided expression is:

$\frac{\left(6\times3\right)^7}{\left(3\times6\right)^2}$

The power of a quotient rule states:

$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

First, simplify the terms inside the parentheses:

Thus, the expression simplifies to:

$\frac{18^7}{18^2}$

We can simplify this further using the rule of dividing powers with the same base:

$\frac{a^m}{a^n} = a^{m-n}$

Apply the rule:

$\frac{18^7}{18^2} = 18^{7-2} = 18^5$

The solution to the question is:

A+B are correct