Which of the following is an equivalent expression to (2−3 ⋅93)−429 ⋅9−10 with only positive exponents, generated by applying the Properties of Integer Exponents?(1 point)

Question

Responses

2^−7⋅9^-1/2^9⋅9^−10

2^3 ⋅9^2

2^12⋅9^−12/2^9⋅9^−10

2^3/9^2

Answer 1

To rewrite the expression with positive exponents, we can apply the property of negative exponents, where a^(-n) = 1/a^n.

Starting from the original expression:
(2-3 * 9^3)-4^2 * 9^-10

First, apply the property of negative exponents to the 3 in the first term:
(2-3 * (1/9^3))-4^2 * 9^-10

Next, simplify the exponent of 9 in the first term and distribute the exponent of -10 to both the 4 and 9 in the second term:
(2-3 * 1/729)-4^2 * (1/9^10)

Now, simplify the numerical values in the first term:
(2-1/243)-4^2 * (1/9^10)

Next, simplify the exponent of 4 in the second term:
(2-1/243)-16 * (1/9^10)

Now, simplify the numerical values in the second term:
(2-1/243)-16/9^10

Finally, rewrite the exponents with positive values:
2^1-1/3^5-16/3^20

So, the equivalent expression with only positive exponents is 2^1-1/3^5-16/3^20.