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
Here are the solutions for problems 6 and 7: 6. Simplify, and write as an index notation: 3 × 3 × 3 × (1)/(3) × 3 × (1)/(3) Step 1: Rewrite the fractions as powers with a negative exponent. Recall that (1)/(a) = a^-1. So, (1)/(3) = 3^-1. The expression becomes: 3^1 × 3^1 × 3^1 × 3^-1 × 3^1 × 3^-1 Step 2: Apply the exponent rule a^m × a^n = a^m+n to combine the terms. Add all the exponents: 1 + 1 + 1 + (-1) + 1 + (-1) = 3 - 1 + 1 - 1 = 2 Step 3: Write the simplified expression in index notation. 3^2 The simplified expression in index notation is: 3^2 7. Evaluate: ((13^0)/(5))^2 Step 1: Evaluate the term 13^0. Any non-zero number raised to the power of 0 is 1. 13^0 = 1 Step 2: Substitute this value back into the expression. ((1)/(5))^2 Step 3: Apply the exponent to both the numerator and the denominator. (1^2)/(5^2) Step 4: Calculate the values. (1 × 1)/(5 × 5) = (1)/(25) The evaluated expression is: (1)/(25) Last free one today — make it count tomorrow, or type /upgrade for unlimited.