Simplify the expression (43 × 8 × 162)/(25) and express it in the form 2ⁿ.

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Express all numbers in the expression as powers of 2. We have 4 = 2², 8 = 2³, and 16 = 2⁴. Step 2: Substitute these powers into the given expression. (4³ × 8 × 16²)/(2⁵) = ((2²)³ × 2³ × (2⁴)²)/(2⁵); Step 3: Apply the power rule (a^m)ⁿ = a^(m × n) to simplify the terms in the numerator. (2^(2 × 3) × 2³ × 2^(4 × 2))/(2⁵) = (2⁶ × 2³ × 2⁸)/(2⁵); Step 4: Apply the product rule a^m × aⁿ = a^(m+n) to combine the terms in the numerator. (2⁶⁺³⁺⁸)/(2⁵) = (2¹⁷)/(2⁵); Step 5: Apply the quotient rule (a^m)/(aⁿ) = a^(m−n) to simplify the expression. 2¹⁷⁻⁵ = 2¹² The expression in the form 2ⁿ is 2¹². The final answer is 2¹².

Simplify the expression (43 x 8 x 162)/(25) and express it in the form 2ⁿ.

Answer

Step-by-step solution

Express all numbers in the expression as powers of 2.

Substitute these powers into the given expression.

Apply the power rule $(a^m)^n = a^{m \times n}$ to simplify the terms in the numerator.

Apply the product rule $a^m \times a^n = a^{m+n}$ to combine the terms in the numerator.

Apply the quotient rule $\frac{a^m}{a^n} = a^{m-n}$ to simplify the expression.

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