Question

(6^3)4*6^5 -------------- = (6^7)^2

Answer 1

6^12 * 6^5 / 6^14 = 6^17/6^14 = 6^3= 6*6*6=216

Answer 2

Let's simplify the left-hand side (LHS) of the equation first:

(6^3) * 4 * (6^5)

To simplify this expression, we can use the rule that states "when you multiply numbers with the same base, you add the exponents." So, for (6^3) * (6^5), we add the exponents (3 + 5) to get 6^8:

(6^3) * (6^5) = 6^(3+5) = 6^8

Now, the expression becomes:

6^8 * 4

Next, we can use the rule that states "when you multiply a number with an exponent by another number, you distribute the exponent to each number." So, 6^8 * 4 becomes:

4 * 6^8 = 4 * (6^8)

Now, let's simplify the right-hand side (RHS) of the equation:

(6^7)^2

To simplify this expression, we apply the rule that states "when you raise a number with an exponent to another exponent, you multiply the exponents." So, (6^7)^2 becomes:

6^(7*2) = 6^14

Now, the equation becomes:

4 * (6^8) = 6^14

We can see that the bases on both sides of the equation are the same (6), and since the bases are the same, the exponents must also be equal to satisfy the equation:

8 = 14

However, 8 is not equal to 14. Therefore, the original equation (6^3 * 4 * 6^5 = (6^7)^2) is not true. There might be an error or misunderstanding in the original equation. Double-check the expression or provide more context if necessary.