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 can rewrite the expression as:
3^(-17) / 8^(-14)
Using the property that a^(-n) = 1 / a^n, we can rewrite the expression as:
1 / (3^17) / (1 / (8^14))
Simplifying further, we get:
1 / (3^17) * (8^14)
Therefore, the expression with positive exponents only is:
(8^14) / (3^17)
To apply the property of negative integer exponents and convert the given expression to one with positive exponents only, you can reciprocate the base with its exponent.
Therefore,
3^(-17) / 8^(-14)
can be written as
(1 / 3^17) / (1 / 8^14)
Next, using the division of fractions rule (where a / b = a * (1 / b)), the expression becomes:
1 * (8^14 / 3^17)
This is the final expression equivalent to 3^(-17) / 8^(-14) with positive exponents only.
To apply the property of negative integer exponents, we can take the reciprocal of both the numerator and denominator. By doing so, the negative exponents will become positive exponents.
So for the expression 3^−17/8^−14, we can rewrite it as:
1 / (3^17) / (1 / 8^14)
To simplify further, we can multiply the numerator and denominator by the reciprocal of the denominator:
1 / (3^17) * (8^14 / 1)
Now, let's simplify each term.
In the numerator, raising 3 to the power of 17 will give us a large number. However, since the question asks for a simplified expression, we can't calculate it exactly. Instead, we can leave it as 3^17.
In the denominator, raising 8 to the power of 14 will give us another large number. Again, we can leave it as 8^14.
Putting it all together, the expression equivalent to 3^−17/8^−14 with positive exponents only is:
8^14 / 3^17