What does 6^2 * 6^5=
Exponent rules, also known as power rules, provide guidelines and formulas for simplifying expressions involving exponents. Here are some key exponent rules:
1. Product Rule: When multiplying powers with the same base, add the exponents. For example, a^m * a^n = a^(m+n).
2. Quotient Rule: When dividing powers with the same base, subtract the exponents. For example, a^m / a^n = a^(m-n).
3. Power Rule: When raising a power to another exponent, multiply the exponents. For example, (a^m)^n = a^(m*n).
4. Zero Exponent Rule: Any non-zero number raised to the power of zero is equal to 1. For example, a^0 = 1.
5. Negative Exponent Rule: An exponent of -n can be converted to the reciprocal of the base raised to the exponent n. For example, a^-n = 1/a^n.
6. Product to Power Rule: When a product is raised to an exponent, each factor is raised to that exponent. For example, (ab)^n = a^n * b^n.
7. Quotient to Power Rule: When a quotient is raised to an exponent, the numerator and denominator are each raised to that exponent. For example, (a/b)^n = a^n / b^n.
These exponent rules are helpful for simplifying and evaluating expressions involving exponents, making calculations easier and more efficient.
6^2 * 6^5 = 6^(2+5) = 6^7
can you show the process
Sure! Here's the step-by-step process:
First, we have 6 raised to the power of 2, which is 6^2. This means we have 6 multiplied by itself twice: 6^2 = 6 * 6 = 36.
Next, we have 6 raised to the power of 5, which is 6^5. This means we have 6 multiplied by itself five times: 6^5 = 6 * 6 * 6 * 6 * 6 = 7776.
Now, we can multiply these two results together: 36 * 7776 = 279936.
Therefore, 6^2 * 6^5 = 279936.
the answer 6^2 * 6^5=36^7 is incorrect, how did they get the answer of 36^7?
Apologies for the incorrect response. Let's go through the correct process:
We have 6^2 * 6^5.
To multiply powers with the same base, we add the exponents. So, 6^2 * 6^5 = 6^(2+5).
Adding 2 and 5, we get 6^7.
Therefore, 6^2 * 6^5 simplifies to 6^7.