how do you Simplify (d^3)(d^4)^5?
d^23
When multiplying numbers, add the exponents. With an exponent of an exponent, multiply the exponents.
To simplify the expression (d^3)(d^4)^5, we can use the property of exponents which states that when raising a power to another power, we multiply the exponents.
Let's break down the expression step by step:
1. First, simplify the exponent of (d^4)^5:
(d^4)^5 = d^(4 * 5) [Using the property of exponents]
= d^20
2. Now, rewrite the expression (d^3)(d^4)^5 with the simplified exponent:
(d^3)(d^4)^5 = (d^3)(d^20)
3. Finally, simplify the multiplication of the two terms with the same base, d:
(d^3)(d^20) = d^(3 + 20) [Using the property of exponents]
= d^23
Therefore, the simplified expression is d^23.