Question

raj is simplifying \\((5^4)^3\\) using these steps:

\\((5^4)^3 = 5^4 \cdot 5^4 \cdot 5^4 = 5^{4+4+4}

although raj is correct so far, which step could he have used instead to simplify the expression \\((5^4)^3\\)?

\\(5^{4 \times 3} = 5^{12}\\)
\\(5^{4+3} = 5^7\\)
\\(4^{5 \times 3} = 4^{15}\\)
\\(4^{5+3} = 4^8\\)

Explanation:

Identify the given expression and rule

$$ (5^4)^3 $$

Apply the power of a power rule

$$ (a^m)^n = a^{m \times n} $$

$$ (5^4)^3 = 5^{4 \times 3} = 5^{12} $$

Match with the given options

$$ 5^{4 \times 3} = 5^{12} $$

Answer:

• (A) \(5^{4\times3} = 5^{12}\) (Correct answer)
• (B) \(5^{4+3} = 5^7\)
• (C) \(4^{5\times3} = 4^{15}\)
• (D) \(4^{5+3} = 4^8\)