apply the property of negative integer exponent to generate an expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only
To apply the property of negative integer exponent, we can rewrite the expression by moving the negative exponents to the denominator and changing their signs.
The expression 3^(-17) divided by 8^(-14) is equivalent to (1/3^17) divided by (1/8^14).
To convert the negative exponent to positive, we take the reciprocal of the base.
So, the expression can be rewritten as (1/(3^17)) divided by (1/(1^14 x 8^14)).
Since any number raised to the power of 1 is equal to the number itself, we can simplify further to get:
1/(3^17) divided by (1/(8^14)).
Finally, when we divide by a fraction, we multiply by the reciprocal of that fraction.
Therefore, the expression is equivalent to (1/(3^17)) times (8^14).
So, the expression with positive exponents only is 8^14 divided by 3^17.
To apply the property of negative integer exponents and obtain an expression equivalent to \(3^{-17} \div 8^{-14}\) with positive exponents only, we can reciprocate both terms and change the signs of the exponents. Starting with the given expression:
\(3^{-17} \div 8^{-14}\)
By reciprocating both terms, we get:
\(\frac{1}{3^{17}} \div \frac{1}{8^{14}}\)
To change the signs of the exponents, we can rewrite the expression as:
\(\frac{8^{14}}{3^{17}}\)
Therefore, the expression equivalent to \(3^{-17} \div 8^{-14}\) with positive exponents only is \(\frac{8^{14}}{3^{17}}\).
To apply the property of negative integer exponents and generate an expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only, you can follow these steps:
1. Start with the given expression:
3^(-17) / 8^(-14)
2. Apply the property of negative exponents, which states that a number raised to a negative exponent can be rewritten as its reciprocal raised to the positive exponent.
Rewrite 3^(-17) as 1 / 3^17 and rewrite 8^(-14) as 1 / 8^14.
Now our expression becomes:
(1 / 3^17) / (1 / 8^14)
3. When dividing fractions, you can multiply the numerator by the reciprocal of the denominator.
In this case, instead of dividing by 1 / 8^14, we can multiply by the reciprocal, which is 8^14 / 1.
The expression becomes:
(1 / 3^17) * (8^14 / 1)
4. Simplify the expression by multiplying the numerators together and the denominators together.
The numerator is 1 * 8^14 = 8^14, and the denominator is 3^17.
The simplified expression is:
8^14 / 3^17
Therefore, the expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only is 8^14 / 3^17.