Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7−3⋅7−5 with positive exponents only.(1 point)
7−3⋅7−5=
To apply the Property of Negative Integer Exponents and generate an expression with positive exponents only, we can rewrite it as:
7^(-3) * 7^(-5)
According to the Property of Negative Integer Exponents, we know that when multiplying two numbers with the same base but different negative exponents, we can add the exponents:
7^(-3) * 7^(-5) = 7^(-3 + (-5))
Simplifying the exponents:
= 7^(-8)
To make the exponent positive, we can rewrite it as:
= 1/7^8
So, the expression equivalent to 7^(-3) * 7^(-5) with positive exponents only is 1/7^8.
To apply the property of negative integer exponents, we can rewrite any base raised to a negative exponent as the reciprocal of the base raised to the positive value of the exponent.
Starting with the expression 7^(-3) * 7^(-5), we can rewrite it as:
1/7^3 * 1/7^5
Since 7^3 means 7 raised to the power of 3, we have:
1/343 * 1/16807
Simplifying the fractions:
1/343 = 1/7^3
1/16807 = 1/7^5
Therefore, the expression 7^(-3) * 7^(-5) is equivalent to:
1/7^3 * 1/7^5