Question

3^-17/8^-14=

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this expression, we can apply the exponent property that states when dividing two numbers with the same base, we subtract the exponents.

Therefore, 3^-17/8^-14 can be rewritten as:

(3/8)^(-17) * 8^14

Now we can simplify further by calculating the value inside the parentheses:

3/8 = (2 * 3)/(2 * 4) = (1/2) * (3/4) = 3/8

So the expression becomes:

(3/8)^(-17) * 8^14 = (3/8)^(-17) * 2^14 * 2^14

Now we can apply the exponent property that states when raising a number to a negative exponent, we flip the base and make the exponent positive.

Therefore:

(3/8)^(-17) = (8/3)^17

So the expression simplifies to:

(8/3)^17 * 2^14 * 2^14

Now we can multiply the exponents of 2 to simplify further:

2^(14+14) = 2^28

Finally, the expression becomes:

(8/3)^17 * 2^28

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the expression 3^-17/8^-14, we can use the properties of exponents.

Step 1: Start by simplifying the expression using the rule that states a^-b = 1/a^b.

3^-17/8^-14 can be rewritten as (1/3^17)/(1/8^14).

Step 2: To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

So, (1/3^17)/(1/8^14) can be rewritten as (1/3^17)*(8^14/1).

Step 3: Simplify the expression by applying the rule that states (a^m)/(a^n) = a^(m-n).

1/3^17 equals 3^(-17) and 8^14 equals (2^3)^14, which can be simplified as 2^(3*14).

So, (1/3^17)*(8^14/1) can be rewritten as 3^(-17)*(2^(3*14)/1).

Step 4: Apply the rule for multiplying exponents:

3^(-17)*(2^(3*14)/1) equals 3^(-17)*(2^42).

Step 5: Simplify the expression by multiplying the coefficients and adding the exponents of the same base.

Finally, we have the answer: 3^(-17)*(2^42).

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem, we can use the quotient rule of exponents, which states that when dividing two numbers with the same base, we subtract the exponents.

In this case, we have:

3^-17 / 8^-14

Using the quotient rule, subtract the exponent of the denominator (8^-14) from the exponent of the numerator (3^-17):

3^-17 - (-14)

When subtracting a negative number, we can rewrite it as addition:

3^-17 + 14

Now, we can simplify the expression:

3^-17 + 14 = 1/3^17 + 14

To calculate 1/3^17, we can use the power rule of exponents, which states that when a number is raised to a negative exponent, we can rewrite it as 1 divided by that number raised to the positive exponent:

1/3^17 = 1/(3^17)

Finally, 3^-17/8^-14 is equal to:

1/(3^17) + 14