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Chapter 2: Problem 4

Simplify. \(\left(d^{5}\right)^{3}\left(d^{2}\right)^{4}\)

Short Answer

Expert verified
The simplified expression is \(d^{23}\).

Step by step solution

01

Use the Power Rule

We can simplify each individual term using the power rule (a^m)^n = a^(mn). Apply this to each term: \( \left(d^5\right)^3 = d^{(5 \cdot 3)} = d^{15} \) \( \left(d^2\right)^4 = d^{(2 \cdot 4)} = d^8 \) Now our expression looks like: \( d^{15}d^8 \)
02

Use the Product Rule

We can now simplify the expression by using the product rule, a^m * a^n = a^(m+n). In our case, we have: \( d^{15}d^8 = d^{(15+8)} = d^{23} \) The simplified expression is \(d^{23}\).

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