Why is 5^9 • 5^-13 = 5^4 wrong?
The expression 5^9 • 5^-13 is not equal to 5^4. Let's break down the calculation to understand why:
5^9 • 5^-13 can be written as (5^9)/(5^13). When dividing two exponents with the same base, you subtract the exponents. So, (5^9)/(5^13) simplifies to 5^(9-13) or 5^-4.
Now, 5^-4 means taking the reciprocal of 5^4, which is 1/(5^4) or 1/625.
Therefore, 5^9 • 5^-13 = 1/625, which is not equal to 5^4.
To understand why the equation 5^9 • 5^-13 = 5^4 is incorrect, we need to use the properties of exponents. When multiplying two numbers with the same base, you add their exponents. Therefore, 5^9 multiplied by 5^-13 can be rewritten as 5^(9 + (-13)) or 5^(-4).
However, 5^(-4) is not equal to 5^4. Negative exponents indicate the reciprocal of the base raised to a positive exponent. In this case, 5^-4 means 1/5^4. Therefore, the correct simplification of 5^9 • 5^-13 is 5^(-4) or 1/5^4, not 5^4.
To understand why the equation 5^9 • 5^-13 = 5^4 is incorrect, we need to review the rules of exponents.
In this equation, we have two terms: 5^9 and 5^-13. To multiply these terms, we add the exponents since they have the same base (which is 5). The rule states that when you multiply two terms with the same base, you add their exponents.
So when we multiply 5^9 and 5^-13, we get 5^(9 + (-13)). Simplifying further, 9 + (-13) is equal to -4, so the equation becomes 5^-4.
Now, let's compare this to the right side of the equation, 5^4. This expression represents 5 raised to the power of 4.
The problem is that 5^-4 is not equal to 5^4. The rule for negative exponents states that x^-n is equal to 1 / x^n. So when we have 5^-4, it means 1 / 5^4.
Therefore, the equation 5^9 • 5^-13 = 5^4 is incorrect. The correct equation would be 5^9 • 5^-13 = 5^-4, where 5^-4 is the same as 1 / 5^4.