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The value of 3 to 21 power is how many times as great as the value of 3 to 19 power?

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Final answer:

The value of 3 to the 21st power is 9 times as great as the value of 3 to the 19th power.

Step-by-step explanation:

The question asks how many times greater the value of 3 to the 21st power (321) is compared to the value of 3 to the 19th power (319). To find this, we can use the properties of exponents. Since both expressions have the same base, we can divide them to simplify the comparison:



321 / 319 = 321-19 = 32



So, 321 is 3 to the 2nd power, or 9 times, as great as 319.

To find the value of 3 to the power of 21 compared to the value of 3 to the power of 19, we can calculate each power:

3^21 = 3 × 3 × 3 × ... × 3 (21 times)

3^19 = 3 × 3 × 3 × ... × 3 (19 times)

Since both calculations involve multiplying 3 by itself multiple times, we can see that the value of 3^21 is greater than the value of 3^19 because there are more multiplications involved. Therefore, the value of 3^21 is greater than the value of 3^19.

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