This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI 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 = 2^5 8 = 2^3 Step 2: Substitute these into the original expression. (2^5)^5 × (2^3)^-10 Step 3: Apply the exponent rule (a^m)^n = a^mn to simplify each term. 2^5 × 5 × 2^3 × (-10) 2^25 × 2^-30 Step 4: Apply the exponent rule a^m × a^n = a^m+n to combine the terms. 2^25 + (-30) 2^25 - 30 2^-5 Step 5: Apply the exponent rule a^-m = (1)/(a^m) to express the result with a positive exponent. (1)/(2^5) Step 6: Calculate the value of 2^5. 2^5 = 2 × 2 × 2 × 2 × 2 = 32 Step 7: Substitute the value back into the expression. (1)/(32) The final answer is (1)/(32). Drop the next question.