Answer :
Final answer:
The expression x⁻⁴ * x^(9) simplifies to x^5 by using the rules of exponents. When multiplying terms with the same base, the exponents add up. Hence, in this case, -4 (the exponent of the first term) added to 9 (the exponent of the second term) equals 5.
Explanation:
Listed below are exponential rules that will help us answer your question:
- When the bases are the same, we can add the exponents when multiplying and subtract when dividing.
- Exponents distribute over multiplication and division, not addition and subtraction.
- A negative exponent represents a reciprocal. Specifically, x^-n = 1/x^n.
Now, let's simplify your expression x⁻⁴ * x^(9). In the multiplication of two exponents with the same base, you add up the exponents. Therefore, x^-4 * x^9 can be written as x^(-4+9) or x^5.
Exponential Law
The exponential law being applied here is the multiplication rule, which states that when you're multiplying the same base numbers, you can keep the base the same and add their exponents. This rule is extended to allow the addition of a negative and a positive exponent.
Learn more about Exponential Rules here:
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