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 exponents, we can rewrite the given expression as the reciprocal of the expression with positive exponents.
So,
3^-17/8^-14
is equivalent to
(1/3^17)/(1/8^14).
Now, to get rid of the negative exponents, we can flip the fractions:
(8^14)/(3^17).
Therefore, 3^-17/8^-14 = (8^14)/(3^17).
Apply the Properties of Integer Exponents to generate equivalent expressions to (7^-3) x 7^20/6^-2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
(7^-3) x 7^20/6^-2 =
To simplify the expression and apply the properties of integer exponents, we can combine the terms with the same base:
(7^-3) x 7^20/6^-2 = 7^(-3 + 20) / 6^-2
Simplifying the exponents:
7^17 / 6^-2
Now, to get rid of the negative exponent in 6^-2, we can flip the fraction:
7^17 / (1/6^2)
Simplifying further:
7^17 / (1/36)
To divide by a fraction, we can multiply by its reciprocal:
7^17 * 36 / 1
Now, we can simplify the expression by raising 7 to the 17th power:
(7^17 * 36) / 1 = (832,533,856 * 36) / 1
Multiplying:
= 29,950,981,376 / 1
Therefore, the expression (7^-3) x 7^20/6^-2 is equivalent to the improper fraction 29,950,981,376/1.
simplify last one
I apologize for the confusion. The expression can be simplified further.
(7^17 * 36) / 1 simplifies to 252^17.
Therefore, the simplified expression is 252^17.
make 252^17 an improper fraction
To convert 252^17 into an improper fraction, we can write it as a fraction with a numerator and denominator.
252^17 can be written as 252^17/1.
Therefore, 252^17 is already in the form of an improper fraction.