Negative Exponents Assignment

Find the value of a that makes the statement true. 3^-1/3^4 = 3^a

a = -5

Which of the following expressions are equivalent to 6^-3?

A. 1/6^3 D. 1/216

Select all of the expressions that are equal to the products of 10x^9 and (60x^-6)^-1 Assume x does not equal 0.

A. 10x^9/60x^-6 C. x^15/6

Which of the following expressions are equivalent to 4^-3/4^-8

A. 4^-3/4^8 D. 4^5

Simplify (5n^4)^-3 Assume n isn't equal 0.

B. 1/125n^12

Simplify (2^3)^-2

B. 1/64

Simplify 15y^-7/18y^-3 Assume y is not equal to 0.

B. 5/6y^4

What is the product of 4^4(4^-7)(4)?

C. 1/16

Simplify the quotient 3^-1/3^4

C. 1/243

Smplify 12y^7/18y^-3 Assume y is not equal to 0.

C. 2y^10/3

Simplify (10^-2/10^3)^-1

D. 100,000

Simplify -3d^8(-4d^-14). Assume d is not equal 0.

D. 12/d^6

Write the expression 4^4(4^-7)(4) using a single exponent.

D. 4^-2

Javier simplified the expression below. Find and describe the three mistakes he made. (20x/5x^8)^-3 = (20x)^-3/(5x^8)^-3 = (5x^8)^3/(20x)^3 = 5x^24/20x^4 = x^6/4

Javier did not raise the coefficients to the third power. When Javier raised x to the third power, he wrote that (x^1)^3 = x^4, but it equals x^3. In the last step, Javier divided the exponents. He should have used the quotient of powers property and subtracted them.