Asked by lol
Apply the Properties of Integer Exponents to generate an equivalent expression to (5−3)^6⋅ 5^17/10^−2
Answers
Answered by
GPT 3.5
To apply the properties of integer exponents, we need to break down and simplify each individual exponent expression.
First, simplify (5−3)^6. According to the property (a−b)^n = a^n / b^n, we can rewrite this as 2^6.
Next, simplify 5^17. Since the base (5) remains the same, we can use the property (a^m)^n = a^(m*n) to rewrite this as 5^(6*2+1).
Finally, simplify 10^−2. The negative exponent property states that a^(-n) = 1 / a^n. Therefore, we can rewrite this as 1 / 10^2.
Combining all these simplifications, we have:
(5−3)^6⋅ 5^17/10^−2 = 2^6 * 5^(6*2+1) / (1 / 10^2).
Now, we can simplify further:
2^6 = 64.
5^(6*2+1) = 5^(12+1) = 5^13.
1 / 10^2 = 1 / 100 = 0.01.
Substituting these values back in:
(5−3)^6⋅ 5^17/10^−2 = 64 * 5^13 / 0.01.
This expression can be simplified further, but without additional context or requirements, this is the equivalent expression using the properties of integer exponents.
First, simplify (5−3)^6. According to the property (a−b)^n = a^n / b^n, we can rewrite this as 2^6.
Next, simplify 5^17. Since the base (5) remains the same, we can use the property (a^m)^n = a^(m*n) to rewrite this as 5^(6*2+1).
Finally, simplify 10^−2. The negative exponent property states that a^(-n) = 1 / a^n. Therefore, we can rewrite this as 1 / 10^2.
Combining all these simplifications, we have:
(5−3)^6⋅ 5^17/10^−2 = 2^6 * 5^(6*2+1) / (1 / 10^2).
Now, we can simplify further:
2^6 = 64.
5^(6*2+1) = 5^(12+1) = 5^13.
1 / 10^2 = 1 / 100 = 0.01.
Substituting these values back in:
(5−3)^6⋅ 5^17/10^−2 = 64 * 5^13 / 0.01.
This expression can be simplified further, but without additional context or requirements, this is the equivalent expression using the properties of integer exponents.
Answered by
lol
Apply the Properties of Integer Exponents to generate an equivalent expression to (5−3)^6⋅ 5^17/10^−2
1. 1/20
2. 1/500
3. 20
4. 500
1. 1/20
2. 1/500
3. 20
4. 500
Answered by
GPT 3.5
To generate an equivalent expression using the properties of integer exponents for (5−3)^6⋅ 5^17/10^−2, let's break down and simplify each part separately:
1. Simplify (5−3)^6. According to the exponentiation property (a−b)^n = a^n / b^n, this can be rewritten as 2^6 = 64.
2. Simplify 5^17. Since the base remains the same (5), we can use the exponentiation property (a^m)^n = a^(m*n) to rewrite this as 5^(6*2+1) = 5^13.
3. Simplify 10^−2. Using the negative exponent property, we have 10^(-2) = 1 / 10^2 = 1/100 = 0.01.
Now, substitute the simplified expressions back into the original expression:
(5−3)^6⋅ 5^17/10^−2 = 64 * 5^13 / 0.01.
Further simplifying:
64 * 5^13 / 0.01 = 64 * 5^13 * 100 = 64 * 5^13 * 100.
The final equivalent expression is 64 * 5^13 * 100. However, this answer does not match any of the given options. Please check the problem statement or confirm if any of the given options are correct.
1. Simplify (5−3)^6. According to the exponentiation property (a−b)^n = a^n / b^n, this can be rewritten as 2^6 = 64.
2. Simplify 5^17. Since the base remains the same (5), we can use the exponentiation property (a^m)^n = a^(m*n) to rewrite this as 5^(6*2+1) = 5^13.
3. Simplify 10^−2. Using the negative exponent property, we have 10^(-2) = 1 / 10^2 = 1/100 = 0.01.
Now, substitute the simplified expressions back into the original expression:
(5−3)^6⋅ 5^17/10^−2 = 64 * 5^13 / 0.01.
Further simplifying:
64 * 5^13 / 0.01 = 64 * 5^13 * 100 = 64 * 5^13 * 100.
The final equivalent expression is 64 * 5^13 * 100. However, this answer does not match any of the given options. Please check the problem statement or confirm if any of the given options are correct.