8 to the 3rd power times 8 to the negative 5th power
To solve 8 to the 3rd power multiplied by 8 to the negative 5th power, you can use the exponent rule that states, "When multiplying two numbers with the same base but different exponents, add the exponents." Let's break it down step by step:
Step 1: Simplify 8 to the 3rd power.
8 to the 3rd power is calculated as follows:
8 × 8 × 8 = 512
Step 2: Simplify 8 to the negative 5th power.
To convert a positive exponent to a negative exponent, we take the reciprocal (or inverse) of the base. So, 8 to the negative 5th power becomes 1/8 to the 5th power.
1/8 to the 5th power can be calculated as:
(1/8) × (1/8) × (1/8) × (1/8) × (1/8) = 1/32768
Step 3: Multiply the results from Steps 1 and 2.
512 × (1/32768) = 1/64
Therefore, 8 to the 3rd power times 8 to the negative 5th power equals 1/64.