Simplify (7x)^9/(7x): Applying Exponent Division Rules

Question

Insert the corresponding expression:

(7×x)9(7×x)= \frac{\left(7\times x\right)^9}{\left(7\times x\right)}=

Video Solution

Solution Steps

00:00 Simply
00:03 Every number is essentially to the power of 1
00:06 We'll use this formula in our exercise, and raise to the power of 1
00:10 According to exponent laws, dividing powers with equal bases (A)
00:14 equals the same base (A) to the power of the difference of exponents (M-N)
00:20 We'll use the formula for dividing powers in our exercise
00:24 We'll compare terms according to the formula
00:30 We'll keep the base and subtract between the powers
00:45 We'll calculate the difference of the powers
00:49 And this is the solution to the question

Step-by-Step Solution

To solve the expression (7×x)9(7×x) \frac{(7\times x)^9}{(7\times x)} , we can utilize the Power of a Quotient Rule for exponents. According to this rule, for any non-zero number a a and integers m m and n n , the expression aman \frac{a^m}{a^n} can be simplified to amn a^{m-n} .

Applying this rule, we identify the base (7×x)(7\times x) as the variable and analyze the exponents:

  • The numerator is (7×x)9(7\times x)^9, which means the power 9 applies to the term (7×x)(7\times x).
  • The denominator is (7×x)1(7\times x)^1, which implies a power of 1.

Now, we apply the quotient rule:

(7×x)9(7×x)=(7×x)91=(7×x)8 \frac{(7\times x)^9}{(7\times x)} = (7\times x)^{9-1} = (7\times x)^8

Thus, the expression simplifies to (7×x)8 (7\times x)^8 . This is achieved by subtracting the exponent in the denominator from the exponent in the numerator.

The solution to the question is: (7×x)8 (7\times x)^8 .

Answer

(7×x)8 \left(7\times x\right)^8