35 × 8⁻¹⁰

Question

35 × 8⁻¹⁰

ScanSolve AI Tutor · Accepted Answer

Step 1: Express the bases of the powers as powers of the same prime number. Both 32 and 8 can be expressed as powers of 2. 32 = 2⁵; 8 = 2³ Step 2: Substitute these into the original expression. (2⁵)⁵ × (2³)⁻¹⁰ Step 3: Apply the exponent rule (a^m)ⁿ = a^(mn) to simplify each term. 2^(5 × 5) × 2^(3 × (−10)) 2²⁵ × 2⁻³⁰ Step 4: Apply the exponent rule a^m × aⁿ = a^(m+n) to combine the terms. 2²⁵⁺⁽⁻³⁰⁾ 2²⁵⁻³⁰ 2⁻⁵ Step 5: Apply the exponent rule a^(−m) = (1)/(a^m) to express the result with a positive exponent. (1)/(2⁵) Step 6: Calculate the value of 2⁵. 2⁵ = 2 × 2 × 2 × 2 × 2 = 32 Step 7: Substitute the value back into the expression. 1/32 The final answer is 1/32.

35 x 8⁻¹⁰

Answer

Step-by-step solution

Express the bases of the powers as powers of the same prime number.

Substitute these into the original expression.

Apply the exponent rule $(a^m)^n = a^{mn}$ to simplify each term.

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

Apply the exponent rule $a^{-m} = \frac{1}{a^m}$ to express the result with a positive exponent.

Calculate the value of $2^5$ .

Substitute the value back into the expression.

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