The expression 5^9 x 5^13 can be simplified by applying the property of exponents which states that when multiplying two exponential expressions with the same base, you add the exponents.
Therefore, 5^9 x 5^13 is equivalent to 5^(9+13) = 5^22.
So the expression that is generated by applying the Properties of Integer Exponents is 5^22.
Which of the following is an equivalent expression to 5^9 x 5^13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?
4 answers
Which of the following is an equivalent expression to 5^9 x 5^-13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?
To simplify the expression 5^9 x 5^-13, we can apply the property of exponents which states that when dividing two exponential expressions with the same base, you subtract the exponents. In this case, 5^-13 is equivalent to 1/5^13 or 5^-13 = 1/5^13.
Therefore, 5^9 x 5^-13 is equivalent to 5^9 / 5^13 = 5^(9-13) = 5^(-4).
To generate an equivalent expression with only positive exponents, we can again apply the property of exponents which states that a negative exponent can be written as a positive exponent by taking the reciprocal of the base. In this case, 5^-4 is equivalent to 1/5^4 or 5^-4 = 1/5^4.
Therefore, the equivalent expression with only positive exponents is 1/5^4.
Therefore, 5^9 x 5^-13 is equivalent to 5^9 / 5^13 = 5^(9-13) = 5^(-4).
To generate an equivalent expression with only positive exponents, we can again apply the property of exponents which states that a negative exponent can be written as a positive exponent by taking the reciprocal of the base. In this case, 5^-4 is equivalent to 1/5^4 or 5^-4 = 1/5^4.
Therefore, the equivalent expression with only positive exponents is 1/5^4.
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7 answers