Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only.(1 point)
3^−17/8^−14=
To apply the Property of Negative Integer Exponents, we need to move the negative exponents to the denominator and change their signs to make them positive.
So, 3^(-17) becomes 1/3^17 and 8^(-14) becomes 1/8^14.
Therefore, 3^(-17)/8^(-14) = (1/3^17)/(1/8^14).
Now, when we divide by a fraction, we can multiply by its reciprocal. So, we can convert the division into multiplication by taking the reciprocal of the denominator.
(1/3^17)/(1/8^14) = (1/3^17)*(8^14/1).
Simplifying further,
(1/3^17)*(8^14/1) = 8^14/3^17.
Therefore, 3^(-17)/8^(-14) is equivalent to 8^14/3^17.
To apply the property of negative integer exponents, we can rewrite the expression with positive exponents using the following rule:
a^(-n) = 1/(a^n)
Applying this rule to the given expression:
3^(-17) / 8^(-14)
We can rewrite 3^(-17) as 1/(3^17) and 8^(-14) as 1/(8^14):
1/(3^17) / 1/(8^14)
Now, we can simplify this further by multiplying the numerator and denominator by the reciprocal of the divisor:
1/(3^17) * (8^14/1)
This can be written as:
8^14 / 3^17
Therefore, the expression equivalent to 3^(-17) / 8^(-14) with positive exponents only is 8^14 / 3^17.
To apply the property of negative integer exponents, we can rewrite the given expression as follows:
3^(-17) / 8^(-14)
According to the property of negative exponents, any term with a negative exponent can be moved to the opposite side of the fraction and transformed into a positive exponent.
Therefore, we get:
(8^14) / (3^17)
By applying the property of negative exponents, we have generated an expression equivalent to 3^(-17) / 8^(-14) with positive exponents only.