Use the Product Rule of Exponents to simplify the expression 13 ^ 10 * 13 ^ 4 (1 point) 169 ^ 14; 169 ^ 40; 13 ^ 14; 13 ^ 40
To simplify the expression using the Product Rule of Exponents, we add the exponents:
13^10 * 13^4 = 13^(10+4)
Therefore, the simplified expression is 13^14.
To simplify the expression 13^10 * 13^4 using the Product Rule of Exponents, we add the exponents together since the base (13) is the same.
The Product Rule of Exponents states that for any non-zero number a, and any integers m and n, a^m * a^n = a^(m + n).
Therefore, applying the rule to our expression:
13^10 * 13^4 = 13^(10 + 4) = 13^14
So the simplified expression is 13^14.
Therefore, the answer is 13^14.
To simplify the expression 13^10 * 13^4 using the Product Rule of Exponents, you need to remember that when multiplying two exponential terms with the same base, you can add the exponents. Here's how you can solve it step by step:
Step 1: Apply the Product Rule of Exponents
13^10 * 13^4 = 13^(10+4)
Step 2: Simplify the exponent
10 + 4 = 14
Step 3: Write the simplified expression
13^10 * 13^4 = 13^14
Therefore, the simplified expression is 13^14.
Now, let's evaluate the other expressions you mentioned:
169^14: Since 169 is not the same base as 13, you cannot simplify it using the Product Rule of Exponents. Therefore, 169^14 remains as it is.
169^40: Similarly, this expression cannot be simplified using the Product Rule of Exponents.
13^14: This is the same as the simplified expression we obtained earlier, which is 13^14.
13^40: This is another expression that cannot be simplified using the Product Rule of Exponents.
In summary:
- 13^10 * 13^4 simplifies to 13^14.
- 169^14, 169^40, 13^14, and 13^40 cannot be further simplified using the Product Rule of Exponents.