Which of the following is developed to be equivalent to 1/8⁵?

A. 8 1/5
B. 8^-⁵
C. 8⁵
D. 5^-⁸

9 answers

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.