Question

Use a calculator to evaluate the expression. Round your answer to the nearest hundred thousandth. $$55 \cdot 5^{-6}$$

Short answer

The rounded result of the expression \(55 \cdot 5^{-6}\) to the nearest hundred thousandth is 0.0000176.

Step-by-step solution

Understanding the exponent

We need to understand that \(5^{-6}\) means 1 divided by \(5^{6}\). In general, any number to the power of -n equals 1 divided by that number to the power of n.

Calculate \(5^{-6}\)

Now we calculate \(5^{-6}\) using a calculator. You should get 0.00000032.

Multiply by 55

Multiply the result from Step 2 by 55. Use a calculator to do this. 0.00000032 multiplied by 55 equals 0.0000176.

Round to the nearest hundred thousandth

The result in Step 3 is already in the hundred thousandth place, and no rounding is necessary. Therefore, the final answer is as obtained in Step 3, which is 0.0000176.