Which of the following is developed to be equivalent to 1/8⁵?
A. 8 1/5
B. 8^-⁵
C. 8⁵
D. 5^-⁸
The correct answer is: C. 8⁵.
Which of the following is equivalent to 6^-²?
A. 1/6^-2
B. 1/2⁶
C. 36
D. 1/36
The correct answer is: D. 1/36.
Which of the following is an equivalent expression to 13^-5 • 13^-11 with only positive exponents, generated by applying the properties of exponents?
A. 1/26⁶
B. 1/13¹⁶
C. 1/13⁶
D. 1/26¹⁶
To simplify the expression 13^-5 • 13^-11 with positive exponents, we can apply the property of exponents that states when you multiply two numbers with the same base, you add their exponents.
So, 13^-5 • 13^-11 is equivalent to 13^(-5 + -11).
Simplifying the exponent, we get 13^-16.
Therefore, the equivalent expression with positive exponents is: 1/13^16.
The correct answer is: B. 1/13¹⁶.
Which of the following is an equivalent expression to 14^-⁷/9^-13 with only positive exponents, generated by applying the property of negative integer exponents?
A. 14⁷/9¹³
B. 14^-7 • 9¹³
C. 9¹³/14⁷
D. 1/9¹³•14^-⁷
To simplify the expression 14^-⁷/9^-13 with positive exponents, we can apply the property of negative integer exponents that states for any non-zero number a, a^-b is equal to 1/a^b.
Applying this property, we can rewrite 14^-⁷ as 1/14^7 and 9^-13 as 1/9^13.
So, we have 1/14^7 divided by 1/9^13.
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the division as multiplication by the reciprocal.
So, 1/14^7 divided by 1/9^13 is equivalent to 1/14^7 multiplied by 9^13/1.
Simplifying further, we get 9^13/14^7.
Therefore, the equivalent expression with positive exponents is: 9¹³/14⁷.
The correct answer is: C. 9¹³/14⁷.
Which of the following is an equivalent expression to 7³/25^-4 with only positive exponents, generated by applying the property of negative integer exponents?
A. 7³/25⁴
B. 25⁴/7³
C. 25⁴/7^-³
D. 7³ • 25⁴
To simplify the expression 7³/25^-4 with positive exponents, we can apply the property of negative integer exponents that states for any non-zero number a, a^-b is equal to 1/a^b.
Applying this property, we can rewrite 25^-4 as 1/25^4.
So, we have 7³ divided by 1/25^4.
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the division as multiplication by the reciprocal.
So, 7³ divided by 1/25^4 is equivalent to 7³ multiplied by 25^4/1.
Simplifying further, we get 7³ • 25^4.
Therefore, the equivalent expression with positive exponents is: 7³ • 25^4.
The correct answer is: D. 7³ • 25⁴.
To determine which of the options is equivalent to 1/8⁵, we can start by understanding the concept of exponential notation.
In exponential notation, a number is written in the form of a base raised to a power. For example, in the expression 8⁵, 8 is the base, and 5 is the exponent or power. This means that we have to multiply 8 by itself five times: 8 × 8 × 8 × 8 × 8.
Now, let's go through each option:
A. 8 1/5:
This can be interpreted as 8 raised to the power of 1/5. However, the fraction 1/5 represents the fifth root of 8, not the fifth power. Therefore, option A is not equivalent to 1/8⁵.
B. 8^-⁵:
The negative sign in front of the exponent indicates the reciprocal or the multiplicative inverse. In this case, it would be the reciprocal of 8 raised to the fifth power. Mathematically, it can be written as 1/(8⁵). Since the given expression is 1/8⁵, option B is not equivalent.
C. 8⁵:
This option is 8 raised to the power of 5. It represents the result of multiplying 8 by itself five times, which is not equivalent to 1/8⁵. Hence, option C is incorrect.
D. 5^-⁸:
Similar to option B, a negative exponent indicates the multiplicative inverse. In this case, we have the reciprocal of 5 raised to the eighth power. However, our original expression is 1/8⁵, so option D is also not equivalent.
After evaluating all the options, we can conclude that none of them is equivalent to 1/8⁵.