Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14 with positive exponents only.(1 point)
3−178−14=
1/3^17 * 1/3^8 = 1/3^(17+8) = 1/3^25
To apply the property of negative integer exponents, we can use the fact that any nonzero number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.
Starting with the expression 3^(-17) * 8^(-14), we can apply the property of negative exponents to rewrite it with positive exponents:
3^(-17) * 8^(-14) = 1/(3^17) * 1/(8^14)
Writing the reciprocal of 3^17 and 8^14 in positive exponent form gives us:
1/(3^17) * 1/(8^14) = 1/3^17 * 1/2^(3*14)
Simplifying the exponent in 2^(3*14) gives:
1/3^17 * 1/2^(3*14) = 1/3^17 * 1/2^(42)
Therefore, the expression 3^(-17) * 8^(-14) with positive exponents only is equivalent to 1/3^17 * 1/2^42.