Apply the Properties of Integer Exponents to generate equivalent expressions to (7−3)^7 x7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the following rules:
1) (a^m)^n = a^(m*n)
2) a^(-n) = 1/a^n
3) a^0 = 1
Let's simplify the expression step by step:
(7^(-3))^7 * 7^20 / 6^(-2)
Using rule 2 for the first part:
(1/7^3)^7 * 7^20 / 6^(-2)
Using rule 1 for the first part:
1/7^(3*7) * 7^20 / 6^(-2)
Simplifying the exponents:
1/7^21 * 7^20 / 6^(-2)
Using rule 2 for the third part:
1/7^21 * 7^20 / (1/6^2)
Simplifying the last part:
1/7^21 * 7^20 * 6^2
Now, let's multiply the numerators and denominators separately.
Numerator: 1 * 7^20 * 6^2 = 7^(20+2) * 6^2 = 7^22 * 6^2
Denominator: 7^21 * 1 = 7^21
Combining the numerator and denominator:
(7^22 * 6^2) / 7^21
Using rule 1 for the numerator:
7^(22-21) * 6^2
Simplifying the exponent:
7^1 * 6^2
Which is equal to:
7 * 6^2
Simplifying:
7 * 36 = 252
Therefore, the answer is 252.
put this as an improper fraction
To write the answer as an improper fraction, we divide the numerator (252) by the denominator (1):
252/1
Therefore, the improper fraction form of the answer is 252.
and
a^n * a^m = a^(m+n)
Apologies for the mistake. You are correct.
The correct property is:
a^n * a^m = a^(m+n)
Thank you for pointing that out.
so
(7−3)^7 x7^20/6^−2
= 4^7 * 7^20 * 6^2 maybe
but perhaps
4^7 * 7^(20/36)
I suspect the problem is mistyped.
You are correct. There seems to be a mistake or typo in the expression you provided:
(7−3)^7 x7^20/6^−2
It appears that the expression between (7-3) and (7^20) is missing an operation or a number. Without that missing element, it is not possible to accurately simplify the expression or provide an answer. Can you please provide the complete and accurate expression?