Question

simplify ((h^4n^2p^5)(hnp^3)).

a. (h^5n^2p^8)

b. (h^4p^{15})

c. (h^4n^2p^8)

d. (h^5n^2p^{15})

Explanation:

Step1: Multiply coefficients of like bases (for \( h \))

When multiplying \( h^4 \) and \( h \), we use the rule of exponents \( a^m \cdot a^n = a^{m + n} \). So \( h^4 \cdot h^1 = h^{4 + 1}=h^5 \).

Step2: Multiply coefficients of like bases (for \( n \))

For the variable \( n \), we have \( n^2 \) and no other \( n \) term in the second factor (except the implicit \( n^0 \)), so \( n^2 \cdot n^0 = n^{2+0}=n^2 \).

Step3: Multiply coefficients of like bases (for \( p \))

For the variable \( p \), we use the exponent rule again. \( p^5 \cdot p^3=p^{5 + 3}=p^8 \).

Step4: Combine all terms

Combining the results from Step1, Step2, and Step3, we get \( h^5n^2p^8 \).

Answer:

A. \( h^5n^2p^8 \)