apply the properties of integer exponent to generate equivalent expressions to (7^-3)*7^20
with only positive exponents then solve the expression provide the answer as an improper fraction
To generate equivalent expressions with positive exponents, we can use the property of integer exponents which states that a^(-n) = 1/a^n.
First, let's rewrite the expression using this property:
(7^-3)*7^20 = 1/(7^3)*7^20
Next, we can use the property of multiplying exponential expressions with the same base, which states that a^n * a^m = a^(n+m):
= 1/(7^(3+20))
Now, we can simplify the exponent:
= 1/(7^23)
To solve the expression, we can calculate 7^23 and express the answer as an improper fraction:
7^23 = 3,200,182,748,371
Therefore, the simplified expression is:
1/3,200,182,748,371 = 1/3200182748371
So the answer is 1/3200182748371, which is an improper fraction.
To simplify the expression (7^-3) * 7^20 using the properties of integer exponents, we can combine the exponents and rewrite it as a positive exponent.
First, recall the property of multiplying exponents with the same base: a^m * a^n = a^(m+n).
Using this property, we can rewrite the expression as: 7^(-3) * 7^20 = 7^(-3 + 20) = 7^17.
Now, to calculate 7^17, we know that any non-zero number raised to the power of 0 is equal to 1. Therefore, we can rewrite 7^17 as (7^1)^17 = 7^17.
Hence, the simplified expression is 7^17.
To calculate this expression and provide the answer as an improper fraction, we have:
7^17 = 1 / 7^(-17)
Now, applying the rule that b^(-n) = 1 / b^n, we can rewrite the expression as:
1 / 7^(-17) = 1 / (1 / 7^17) = 1 * (7^17 / 1) = 7^17
So, the simplified expression and the answer in improper fraction form is 7^17.
To apply the properties of integer exponents, we can use the rule that states "a^m * a^n = a^(m + n)" for any nonzero number "a" and integers "m" and "n".
In our case, we have (7^(-3)) * 7^(20). To simplify this expression, we can add the exponents with the same base of 7, so we have:
7^(-3 + 20)
Now, we can simplify the exponents:
7^(17)
To convert the expression to an improper fraction, we need to write the number as a fraction with a numerator and denominator. The numerator will be the given expression, and the denominator will be 1.
This gives us the improper fraction:
7^(17) / 1
Since any number raised to the power of 0 is equal to 1, we can rewrite the fraction as:
7^(17) / 7^0
Using the property of dividing exponents with the same base, we subtract the exponents:
7^(17 - 0)
This gives us:
7^17
Therefore, the equivalent expression to (7^(-3)) * 7^(20) with only positive exponents is 7^17.