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The mathematical expression that is equivalent to the given expression is [tex]256h^{28} k^{8}[/tex].
Given the following data:
To determine the mathematical expression that is equivalent to the given expression:
In order to solve this mathematical expression, we would apply the Index Law for Powers (fourth law of indices), which states that when the power of a number is raised to another power, the powers (indices) should be multiplied together.
Mathematically, the Index Law for Powers (fourth law of indices) is given by the formula:
[tex](a^m)^n = a^{mn}[/tex]
Where:
Applying this law, we have:
[tex](4h^7k^2)^4 = 4^4 \times (h^{7\times 4}) \times (k^{2\times 4})\\\\(4h^7k^2)^4 = 256 \times h^{28} \times k^{8}\\\\(4h^7k^2)^4 = 256h^{28} k^{8}[/tex]
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Complete Question:
Which expression is equivalent to [tex](4h^7k^2)^4[/tex]?