use the product rule of exponents to simplify 5 to the power of ten times 5 to the power of 5
To simplify 5 to the power of ten times 5 to the power of 5 using the product rule of exponents, we add the exponents when multiplying exponential expressions with the same base.
5^10 * 5^5 = 5^(10+5) = 5^15
Therefore, 5 to the power of ten times 5 to the power of 5 simplifies to 5 to the power of 15.
To simplify the expression 5^10 * 5^5 using the product rule of exponents, you need to add the exponents when multiplying two powers with the same base.
The product rule states that for any positive numbers a and b, and any whole number n, a^n * a^b = a^(n+b).
Applying the product rule to the given expression, we have:
5^10 * 5^5 = 5^(10+5).
Adding the exponents together, we get:
5^10 * 5^5 = 5^15.
Therefore, 5^10 * 5^5 simplifies to 5^15.
To simplify the expression 5^10 * 5^5 using the product rule of exponents, you need to understand the rule.
The product rule of exponents states that when you multiply two powers with the same base, you can add their exponents. It can be written as: a^m * a^n = a^(m+n).
Now let's simplify the given expression:
5^10 * 5^5 = 5^(10+5)
To calculate the sum of exponents, you add the values together: 10 + 5 = 15.
So, 5^10 * 5^5 equals 5^15.
Therefore, the simplified expression is 5 to the power of 15.