Apply All Exponent Rules Quick Check%0D%0A5 of 55 of 5 Items%0D%0A%0D%0AQuestion%0D%0AWhich 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)%0D%0AResponses%0D%0A%0D%0A2392%0D%0AStart Fraction 2 cubed over 9 squared end fraction%0D%0A%0D%0A23 ⋅92%0D%0A2 cubed times 9 squared%0D%0A%0D%0A2−7⋅9−129⋅9−10%0D%0AStart fraction 2 superscript negative 7 baseline times 9 superscript negative 1 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction%0D%0A%0D%0A212⋅9−1229⋅9−10
To solve this problem, we can apply the exponent rules step by step.
First, we have (2−3 ⋅93)−429 ⋅9−10.
Using the power of a product rule, we can simplify the exponent in the parentheses:
(2−3 ⋅93)−429 = 2−3 ⋅ (9^3)−429.
Now we can apply the power of a power rule to simplify the exponent (9^3)−429:
(9^3)−429 = 9^(3⋅29).
Next, we can apply the product of powers rule to simplify the expression: 2−3 ⋅ 9^(3⋅29):
2−3 ⋅ 9^(3⋅29) = 2−3 ⋅ (9^3)^29.
Using the power of a power rule, we can simplify the expression (9^3)^29:
(9^3)^29 = 9^(3⋅29).
Finally, we have 2−3 ⋅ 9^(3⋅29) = 2−3 ⋅ 9^(87).
Now, we have an equivalent expression with only positive exponents: 2−3 ⋅ 9^(87).
The answer is 2−3 ⋅ 9^(87).