Which is an equivalent expression using a positive exponent?
( 3/5 )⁻⁸ ÷ ( 3/5 )⁻⁴
( 3/5 )⁴
( 3/5 )¹²
( 5/3 )³²
( 5/3 )⁴
Which is an equivalent expression using a positive exponent?
![[Deleted User]](https://quizzma.com/wp-content/plugins/WPQA/images/default-image.png "[Deleted User]"){kind=avatar}
Share
Quizzma Latest Questions
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
To simplify the expression ((3/5)^{-8} ÷ (3/5)^{-4}), we can use the property of exponents that states (a^{-m} ÷ a^{-n} = a^{n-m}).
So, we have:
[
(3/5)^{-8} ÷ (3/5)^{-4} = (3/5)^{-8 – (-4)} = (3/5)^{-8 + 4} = (3/5)^{-4}
]
Now, to express it with a positive exponent, we can use the rule (a^{-m} = 1/a^{m}):
[
(3/5)^{-4} = frac{1}{(3/5)^{4}} = (5/3)^{4}
]
Thus, the equivalent expression using a positive exponent is ((5/3)^{4}).
The correct answer is ((5/3)^{4}).
To simplify the expression ((frac{3}{5})^{-8} div (frac{3}{5})^{-4}), we apply the property of exponents which states that (a^{-m} = frac{1}{a^m}) and also the rule for dividing exponents: (a^m div a^n = a^{m-n}).
1. Rewrite the expression as:
[
(frac{3}{5})^{-8} div (frac{3}{5})^{-4} = (frac{3}{5})^{-8 – (-4)} = (frac{3}{5})^{-8 + 4} = (frac{3}{5})^{-4}
]
2. Convert the negative exponent to a positive one:
[
(frac{3}{5})^{-4} = frac{1}{(frac{3}{5})^4} = (frac{5}{3})^{4}
]
Thus, the equivalent expression using a positive exponent is ((frac{5}{3})^{4}).
The correct answer is ((5/3)^{4}).