Question

combine all this into 4 sentencesThe evaluation of the base 4 with the exponents 3, 0, and -2 results in 64, 1, and 0.0625 respectively. ➡️ Step 1: Calculate the positive exponent To evaluate a positive integer exponent, multiply the base by itself the number of times indicated by the exponent:\(4^{3}=4\times 4\times 4=64\)➡️ Step 2: Apply the zero exponent rule Any non-zero base raised to the power of zero is defined as 1 according to the exponent rule \(b^{0}=1\):\(4^{0}=1\)➡️ Step 3: Evaluate the negative exponent To evaluate a negative exponent, use the reciprocal of the base raised to the positive version of that exponent (\(b^{-n}=\frac{1}{b^{n}}\)):\(4^{-2}=\frac{1}{4^{2}}=\frac{1}{16}\)Converting the fraction to a decimal:\(\frac{1}{16}=0.0625\)✅ Answer: The results for base 4 are: \(4^{3}=\mathbf{64}\)\(4^{0}=\mathbf{1}\)\(4^{-2}=\mathbf{0.0625}\)

Answer 1

The evaluations of base 4 with exponents 3, 0, and -2 give 64, 1, and 0.0625 respectively. For the positive exponent, multiply the base by itself: 4^3 = 4 × 4 × 4 = 64. By the zero exponent rule any nonzero base to the power of 0 equals 1, so 4^0 = 1. A negative exponent uses the reciprocal: 4^(−2) = 1/4^2 = 1/16 = 0.0625.