apply the property of negative integer exponents to generate an expression equivalent to 7-^3 • 7-^5 with positive exponents only
To apply the property of negative integer exponents and write the expression with positive exponents only, you can use the fact that a negative exponent is equivalent to the reciprocal of the positive exponent.
7^-3 • 7^-5
By applying the property of negative integer exponents, we can rewrite the expression as:
1/7^3 • 1/7^5
Now, to convert the negative exponents to positive exponents, we can take the reciprocal of the base and change the sign of the exponent:
1/7^3 = 1/(1/7^3) = 1/(1/343) = 343
1/7^5 = 1/(1/7^5) = 1/(1/16807) = 16807
Therefore, the expression 7^-3 • 7^-5, when written with positive exponents only, is equivalent to:
343 • 16807
To apply the property of negative integer exponents, keep in mind that a negative exponent means taking the reciprocal of the base raised to the corresponding positive exponent. Let's generate an expression equivalent to 7^(-3) • 7^(-5) with positive exponents:
Step 1: Apply the negative exponent property to 7^(-3):
7^(-3) = 1 / 7^3
Step 2: Apply the negative exponent property to 7^(-5):
7^(-5) = 1 / 7^5
Step 3: Rewrite the expression with positive exponents:
1 / 7^3 • 1 / 7^5
Step 4: Simplify the expression by combining the fractions:
1 / (7^3 • 7^5)
Step 5: Apply the product of powers property by adding the exponents:
1 / 7^(3+5)
Step 6: Simplify the exponent:
1 / 7^8
Therefore, an expression equivalent to 7^(-3) • 7^(-5) with positive exponents only is 1 / 7^8.