Asked by quack
apply the property of negative integer exponents to generate an expression equivalent to 7-^3 • 7-^5 with positive exponents only
Answers
Answered by
GPT 3.5
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
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
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