Apply the property of negative integer exponents to generate an expression equivalent to 3^-16/8^-14 with positive exponents l only
To apply the property of negative integer exponents, we can rewrite the expression as:
(8^(14)/3^(16))
Now, to generate an equivalent expression with positive exponents only, we can simply take the reciprocal of the expression:
(3^(16)/8^(14))
Therefore, an expression equivalent to 3^-16/8^-14 with positive exponents only is 3^(16)/8^(14).
To apply the property of negative integer exponents and express the given expression with positive exponents only, we can rewrite it as follows:
3^-16/8^-14
Using the property of negative exponents, we can rewrite 3^-16 as 1/3^16 and 8^-14 as 1/8^14:
(1/3^16)/(1/8^14)
Next, we can simplify this expression by multiplying the numerator and denominator by the reciprocal of 1/8^14, which is 8^14:
(1/3^16) * (8^14/1)
Simplifying this further, we multiply the numerators and denominators separately:
(1 * 8^14) / (3^16 * 1)
Therefore, the expression with positive exponents only that is equivalent to 3^-16/8^-14 is:
8^14/3^16
To generate the expression equivalent to 3^-16/8^-14 with positive exponents only, we can apply the property of negative integer exponents. In this property, when a number with a negative exponent is moved to the denominator or numerator of a fraction, the exponent becomes positive.
First, let's substitute 3^-16 and 8^-14 with their reciprocal values:
3^-16 = 1/3^16
8^-14 = 1/8^14
Now, let's substitute these values back into the original expression:
1/3^16 divided by 1/8^14 or (1/3^16) * (8^14/1)
Next, let's simplify the expression by multiplying the numerators and denominators:
1 * 8^14 / 3^16
Since we want the expression to have only positive exponents, let's rewrite it by expressing 8^14 and 3^16 in terms of positive exponents:
8^14 is equivalent to (2^3)^14, which simplifies to 2^42.
3^16 remains the same.
Substituting these values back into the expression, we get:
1 * (2^42) / (3^16)
Therefore, the expression equivalent to 3^-16/8^-14 with positive exponents only is (2^42) / (3^16).