Question

A Polyphemus Moth caterpillar weighs about 1 /64 ^2 times less when it first becomes a larva than it does when it is fully grown. Write this number using a negative exponent.

Answer 1

The number 1 / 64^2 times less expressed using a negative exponent is 64^-2. This is determined by understanding that a negative exponent represents the reciprocal of the base raised to the positive exponent.

Step-by-step explanation:

A Polyphemus Moth caterpillar weighs approximately 1 / 642 times less when it first hatches than when it is fully grown. To express this number using a negative exponent, we rewrite the fraction as a power of 64. The expression 1 / 642 can be written using a negative exponent as 64-2.

Here is the step-by-step conversion:

1. Start with the fraction 1 / 642.
2. Recognize that 642 is the same as 64 × 64.
3. Since we are looking for an expression with a negative exponent, remember that a negative exponent indicates the reciprocal of the base raised to the positive exponent.
4. Therefore, 1 / 642 can be re-written as 64-2.