Apply the product rule of exponents to find the numerical equivalent of 6^-4 x 6^9. Show your work and explain how you use the product rule.
To apply the product rule of exponents (also known as the power rule), we need to multiply the base while adding the exponents.
The product rule states that for any two numbers a and b, with the same base, a^m * a^n = a^(m+n).
In this case, we have 6^-4 * 6^9. Since the base is the same (6), we can use the product rule to simplify this expression.
6^-4 * 6^9 = 6^(-4 + 9) = 6^5
Thus, the numerical equivalent of 6^-4 x 6^9 is 6^5.
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The product rule of exponents states that when multiplying two exponential expressions with the same base, you add their exponents.
To solve the expression 6^-4 x 6^9 using the product rule of exponents, we start by noting that both terms have the same base, which is 6.
Step 1: Write out the expression:
6^-4 x 6^9
Step 2: Apply the product rule of exponents:
6^(-4 + 9)
Step 3: Simplify the exponent:
6^5
Step 4: Calculate the numerical value of 6^5:
6^5 = 6 * 6 * 6 * 6 * 6 = 7776
Therefore, the numerical equivalent of 6^-4 x 6^9 is 7776.
To apply the product rule of exponents to find the numerical equivalent of 6^-4 x 6^9, you need to remember that the product rule states that when multiplying exponential expressions with the same base, you can add the exponents.
Let's start with the expression 6^-4 x 6^9.
Using the product rule, we can add the exponents: (-4) + 9 = 5.
So, the new expression becomes 6^5.
To find the numerical equivalent of 6^5, you need to evaluate it.
Start with 6^1, which is equal to 6.
Then, multiply 6^1 by 6^1 to get 6^2, which is equal to 6 * 6 = 36.
Continue this process until you reach 6^5.
6^2 is equal to 36, so multiplying 36 by 6, we get 6^3 = 36 * 6 = 216.
Next, multiply 216 by 6 again to get 6^4: 216 * 6 = 1296.
Finally, multiply 1296 by 6 to get 6^5: 1296 * 6 = 7776.
Therefore, the numerical equivalent of 6^-4 x 6^9 is 7776.
By using the product rule of exponents, we were able to simplify the expression and calculate its value step by step.